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Mon. Not. R. Astron. Soc. 000, 1–29 (2016) Printed 18 November 2018 (MN LATEX style file v2.2)

The JCMT Gould Belt Survey: First results from

SCUBA-2 observations of the Cepheus Flare Region

K. Pattle1, D. Ward-Thompson1, J.M. Kirk1, J. Di Francesco3,2, H. Kirk3,

J.C. Mottram4,5, J. Keown2, J. Buckle6,7, S.F. Beaulieu8, D.S. Berry9,

H. Broekhoven-Fiene2, M.J. Currie9, M. Fich8, J. Hatchell10, T. Jenness9,11,

D. Johnstone9,3,2, D. Nutter12, J.E. Pineda13,14,15, C. Quinn12, C. Salji6,7, S. Tisi8,

S. Walker-Smith6,7, M.R. Hogerheijde4, P. Bastien16, D. Bresnahan1, H. Butner17,

M. Chen2, A. Chrysostomou18, S. Coude16, C.J. Davis19, E. Drabek-Maunder20,

A. Duarte-Cabral10, J. Fiege21, P. Friberg9, R. Friesen22, G.A. Fuller14,

S. Graves9, J. Greaves12, J. Gregson23,24, W. Holland25,26, G. Joncas27,

L.B.G. Knee3, S. Mairs2, K. Marsh12, B.C. Matthews3,2, G. Moriarty-Schieven3,

C. Mowat10, J. Rawlings28, J. Richer6,7, D. Robertson29, E. Rosolowsky30,

D. Rumble10, S. Sadavoy5, H. Thomas9, N. Tothill31, S. Viti28, G.J. White23,24,

J. Wouterloot9, J. Yates28, M. Zhu32

Affiliations can be found after the references.

ABSTRACT

We present observations of the Cepheus Flare obtained as part of the James ClerkMaxwell Telescope (JCMT) Gould Belt Legacy Survey (GBLS) with the SCUBA-2instrument. We produce a catalogue of sources found by SCUBA-2, and separate theseinto starless cores and protostars. We determine masses and densities for each of oursources, using source temperatures determined by the Herschel Gould Belt Survey. Wecompare the properties of starless cores in four different molecular clouds: L1147/58,L1172/74, L1251 and L1228. We find that the core mass functions for each regiontypically show shallower-than-Salpeter behaviour. We find that L1147/58 and L1228have a high ratio of starless cores to Class II protostars, while L1251 and L1174have a low ratio, consistent with the latter regions being more active sites of currentstar formation, while the former are forming stars less actively. We determine that,if modelled as thermally-supported Bonnor-Ebert spheres, most of our cores havestable configurations accessible to them. We estimate the external pressures on ourcores using archival 13CO velocity dispersion measurements and find that our coresare typically pressure-confined, rather than gravitationally bound. We perform a virialanalysis on our cores, and find that they typically cannot be supported against collapseby internal thermal energy alone, due primarily to the measured external pressures.This suggests that the dominant mode of internal support in starless cores in theCepheus Flare is either non-thermal motions or internal magnetic fields.

Key words: stars: formation – dust, extinction – submillimetre: ISM

1 INTRODUCTION

The Cepheus Flare region is a collection of star-formingmolecular clouds extending to ∼ 10 − 20 degrees above the

Galactic Plane at a Galactic Longitude of ∼ 110 degrees(Hubble 1934). Star formation is occurring at several dif-ferent distances along the line of sight toward the CepheusFlare: at ∼ 160 pc, where star formation is associated with

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2 K. Pattle et al.

Figure 1. A finding chart of the Cepheus region. The greyscale image shows IRAS 100-µm emission (Miville-Deschenes & Lagache2005). The grey contours show AV extinctions of 0.1, 0.5 and 1.0, smoothed with an 8-pixel Gaussian for clarity (Dobashi et al. 2005).The regions enclosed in solid white lines were observed as part of the JCMT GBS (Ward-Thompson et al. 2007). The reflection nebulaL1174/NGC 7023 is marked. The L1172 region is immediately to the south of L1174. The variable star PV Cep and the protostarL1157-mm, both in the L1147/58 region, are also marked. The dashed white line shows the approximate position of the Cepheus FlareShell (K09) – the CFS.

the edge of the Local Bubble; at ∼ 300 pc, associated withthe Gould Belt; and at ∼ 800 pc, associated with the Perseusarm of the Galaxy (Kun, Kiss & Balog 2008, and referencestherein; Kirk et al. 2009, hereafter K09).

The Gould Belt is a ring of molecular clouds and OBassociations ∼ 1 kpc in diameter and inclined ∼ 20 to theGalactic Plane (Herschel 1847; Gould 1879). The Gould Beltis considered a ‘laboratory’ for the study of low-mass starformation, as most of the low-mass star forming regionswithin 500 pc of the Earth are associated with it. As a re-sult, surveys aimed at mapping substantial fractions of theGould Belt have been undertaken using the JCMT (Ward-Thompson et al. 2007), the Herschel Space Observatory(Andre et al. 2010), and the Spitzer Space Telecope (Evanset al. 2009).

In this paper, we present SCUBA-2 observations ofthe intermediate-distance material in Cepheus associatedwith the Gould Belt. These data were taken as part ofthe James Clerk Maxwell Telescope (JCMT) Gould BeltLegacy Survey (GBLS; Ward-Thompson et al. 2007). Thereare five dark cloud complexes in the Cepheus Flare whichare associated with the Gould Belt: L1147/48/52/55/57/58,L1172/74, L1247/51, L1228 and L1241 (Lynds 1962). Wepresent SCUBA-2 data for all or part of each of these re-gions, with the exception of L1241.

The Cepheus Flare is a sparsely-filled region in whichstar formation appears to be proceeding in a variety of differ-

ent environments. IRAS 100µm observations of the CepheusFlare (Miville-Deschenes & Lagache 2005) are shown in Fig-ure 1, with contours of AV extinction overlaid (Dobashi et al.2005). The regions of highest visual extinction are not dis-tributed evenly across the Cepheus Flare, but instead areprincipally located on its north-eastern and south-westernsides. In addition, Cepheus has a central region of relativelylow extinction (AV < 3; Dobashi et al. 2005) in which littlestar formation is occurring, although there is not a completelack of molecular gas or young stars here (Tachihara et al.2005). K09 found that YSOs in the Cepheus Flare are typ-ically found in small, isolated groups, with a much higherfraction of distributed YSOs (the fraction of YSOs not asso-ciated with a group) than is typical: 41% of YSOs in Cepheusare distributed, compared to an average of ∼ 10% acrossclouds observed as part of the Spitzer c2d survey (Evanset al. 2009).

The Cepheus Flare is defined by the interaction of a col-lection of shells with the local ISM, of which the most signifi-cant to the evolution of the region appears to be the CepheusFlare Shell (CFS – Grenier et al. 1989; Olano, Meschin &Niemela 2006), an expanding supernova bubble with a radius∼ 9.5, whose centre is located to the east of the CepheusFlare at Galactic coordinates l ∼ 120, b ∼ 17. The approx-imate position of the CFS is marked on Figure 1. The shelldivides the north-eastern and south-western star-forming re-gions. Olano, Meschin & Niemela (2006) suggest that star

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First SCUBA-2 observations of Cepheus 3

Table 1. Cepheus regions observed as part of the JCMT GBLS, with approximate central positions in equatorial and galactic coordinateslisted.

R.A. (J2000) Dec. (J2000) l b Distance DistanceRegion (hours:min) (deg:arcmin) (deg) (deg) (pc) Reference

L1147/58 21:02 +68:00 104.0 14.1 325± 13 Straizys et al. (1992)L1172/74 20:41 +67:52 102.6 15.6 288± 25 Straizys et al. (1992)

L1251 22:34 +75:14 114.4 14.7 300+50−10 Kun, Kiss & Balog (2008)

L1228 20:58 +77:38 111.7 20.2 200+100−10 Kun, Kiss & Balog (2008)

Figure 2. SCUBA-2 850-µm observations of the L1172 (south)and L1174 (north) regions, with sources marked. The ellipsesshow twice the FWHM size of each source. Contours of Av of0.5, 1.0, 1.5 and 2.0 magnitudes are shown for reference (Dobashiet al. 2005). The dashed line marks approximately the boundarybetween the L1172 and L1174 regions. The position of the HerbigAe/Be star HD200775 is marked.

formation in the eastern regions of the Cepheus Flare hasbeen triggered by the passage of the CFS. K09 note thatthe current position of the CFS is consistent with that ofL1228, and suggest that star formation in this region is be-ing enhanced by the interaction with the shell. A possiblegeometry of the clouds associated with the CFS is proposedby Kun, Kiss & Balog (2008). In this geometry, the variousintermediate-distance dark clouds are located approximatelyon the current surface of the CFS. As the CFS has an ap-proximate radius of ∼ 50 pc and is located at a distance of∼ 300 pc from the Earth (Olano, Meschin & Niemela 2006),there are significant differences, both fractional and abso-lute, between the distances of the various dark clouds asso-ciated with the CFS, despite those dark clouds appearingalong very similar lines of sight. (See Table 1 for distances.)

In this study we identify, and investigate the proper-ties of, starless cores in the Cepheus Flare. We investigatethe cores’ stability against collapse and the relative impor-tance of gravity and external surface pressure in their con-finement. Previous analysis of GBS data of the Ophiuchusmolecular cloud (an intermediate-mass star-forming regionforming stars in a clustered manner; e.g. Wilking, Gagne &Allen 2008) has suggested that dense starless cores in thatregion are typically confined by external surface pressurerather than self-gravity (Pattle et al. 2015). We here inves-tigate whether starless cores in the various different envi-ronments found in the Cepheus Flare behave in a similarmanner.

This paper is laid out as follows. In Section 2, we dis-cuss the observations and data reduction. In Section 3, wediscuss source extraction and characterisation, and presentour catalogue of sources. In Section 4, we discuss the prop-erties of the starless cores in our catalogue. In Section 5,we discuss the counting statistics of starless and protostel-lar sources in Cepheus. In Section 6, we assess the stabilityof our cores using the Bonnor-Ebert criterion. In Section 7,we discuss the energy balance in the starless cores in ourcatalogue, and put an upper limit on the degree to whichthe cores are virially bound. In Section 8, we summarise ourconclusions.

2 OBSERVATIONS

The SCUBA-2 (Holland et al. 2013) observations used hereform part of the JCMT GBLS (Ward-Thompson et al.2007). Continuum observations at 850 µm and 450 µmwere made using fully sampled 30′ diameter circular regions(PONG1800 mapping mode, Kackley et al. 2010) at resolu-tions of 14.1′′ and 9.6′′ respectively. The Cepheus Flare wasobserved with SCUBA-2 in 41 observations taken between2012 March 30 and 2014 October 24. The L1174 field wasobserved four times in very dry (Grade 1; τ225GHz < 0.05)weather. The remainder of the fields were each observed sixtimes in dry (Grade 2; 0.05<τ225GHz<0.08) weather, exceptfor one field, L1147/58 East (containing the star PV Cep,discussed below), which was observed seven times. Larger re-gions were mosaicked with overlapping scans. Four final out-put maps were produced, the central co-ordinates of whichare listed in Table 1.

The data were reduced using an iterative map-makingtechnique (makemap in smurf, Chapin et al. 2013), andgridded to 3′′ pixels at 850 µm and 2′′ pixels at 450 µm, aspart of the Legacy Release 1 (LR1) GBLS data set (see Mairset al. 2015). The iterations were halted when the map pixels,on average, changed by <0.1% of the estimated map rms.The initial reductions of each individual scan were coadded

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4 K. Pattle et al.

Figure 3. SCUBA-2 850-µm observations of the L1147/L1158 region, with sources marked. The ellipses show twice the FWHM size ofeach source. Contours of Av of 0.5, 1.0, 1.5 and 2.0 magnitudes are shown for reference (Dobashi et al. 2005). The protostars PV Cepand L1157-mm are labelled, and the position of the A6V star BD+67 1263 is marked. The boxes mark approximately the extent of theL1152 and L1155 regions.

to form a mosaic from which a mask based on signal-to-noise ratio was produced for each region. The final mosaicwas produced from a second reduction using this mask todefine areas of emission. Detection of emission structure andcalibration accuracy are robust within the masked regions,and are uncertain outside of the masked region.

A spatial filter of 10′ is used in the reduction, whichmeans that flux recovery is robust for sources with a Gaus-sian FWHM less than 2.5′. Sources between 2.5′ and 7.5′

in size will be detected, but both the flux and the sizeare underestimated because Fourier components with scalesgreater than 5′ are removed by the filtering process. Detec-tion of sources larger than 7.5′ is dependent on the maskused for reduction. The mask introduces further spatial fil-tering, as after all but the final iteration of the map-maker,all emission outside the region enclosed by the mask is sup-pressed. Therefore, the recovery of extended structure out-side of the masked regions is limited.

The data are calibrated in mJy/arcsec2, using aper-ture Flux Conversion Factors (FCFs) of 2.34 and 4.71Jy/pW/arcsec2 at 850 µm and 450 µm, respectively, de-rived from average values of JCMT calibrators (Dempseyet al. 2013). The estimated 1 − σ errors on the FCFs are0.08 Jy/pW/arcsec2 and 0.50 Jy/pW/arcsec2 at 850 µm and450 µm respectively. The PONG scan pattern leads to lowernoise levels in the map centre and overlap regions, while data

reduction and emission artifacts can lead to small variationsin the noise level over the whole map.

The SCUBA-2 850-µm data of Cepheus are shownin Figures 2 (L1172/74), 3 (L1147/58), 4 (L1251) and 5(L1228). The sources we extract from the data are marked ascoloured ellipses: light green in L1174, dark green in L1172,red in L1147/58, blue in L1251, and purple in L1228. Thiscolour coding is continued throughout this paper.

The emission measured in the 850-µm filter on SCUBA-2 can be contaminated by the CO J= 3 → 2 transi-tion (Drabek et al. 2012) which, with a rest wavelength of867.6µm, is covered by the SCUBA-2 850-µm filter, whichhas a half-power bandwith of 85 µm (Holland et al. 2013).The only regions in the map which are expected to be sub-stantially CO-contaminated are local to the PV Cep andL1157-mm protostars (discussed in Section 3.1), with whichthere are strong outflows associated (the CO contributionfrom the outflow associated with L1157-mm is clearly visi-ble as extensions north and south of the source in Figures 3and 6, below). However, as can be seen in Figure 3, both PVCep and L1157-mm are isolated objects, and CO emissionfrom their outflows is unlikely to affect the fluxes measuredfor any of the other sources in the field.

Table 2 lists the 1-σ RMS noise levels in each of theregions observed, measured on the default LR1 pixel widthsof 2 arcsec at 450 µm and 3 arcsec at 850 µm. The 450-µm RMS noise levels vary somewhat between different re-

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First SCUBA-2 observations of Cepheus 5

Table 2. The mean 1-σ RMS noise levels in each of the regionsobserved, measured on the default LR1 pixel sizes of 2 arcsec at450µm and 3 arcsec at 850µm.

450-µm RMS 850-µm RMSRegion mJy/sqa mJy/sqa

L1174 1.03± 0.08 0.069± 0.006

L1172 2.16± 0.16 0.056± 0.004L1155 2.44± 0.11 0.056± 0.004L1157 2.20± 0.09 0.055± 0.005

L1251 E 1.77± 0.09 0.059± 0.003L1251 W 0.93± 0.04 0.054± 0.005

L1228 0.87± 0.05 0.059± 0.007

gions observed in the same weather band. This is due tothe differing 450-µm sensitivity across Band 2 weather con-ditions. The 850-µm RMS noise is highest in L1174, de-spite this region having been observed in the best weather,due to the presence of the NGC7023 reflection nebula (seeSection 3.1). The bright, extended emission from NGC7023makes it more difficult for the data reduction process toconverge on a solution.

The 450-µm and 850-µm SCUBA-2 datapresented in this paper are available at:http://dx.doi.org/xx.xxxxx/yy.yyyy.

3 RESULTS

3.1 Cepheus Flare Region

The Cepheus Flare consists of several distinct areas of highcolumn density, each of which is at a different distance andlikely to have a different star formation history. Thus, weconsider each separately in the following analysis, and sum-marise their properties here.

L1172/L1174 is a site of clustered star formation. Thedark cloud L1174, shown in the northern part of Fig-ure 2, is coincident with the NGC7023 reflection neb-ula, also known as the Iris Nebula (Herschel 1802).The nebula is illuminated by the Herbig Ae/Be starHD200775 (R.A. (J2000) = 21h 01m 39.920s, Dec. (J2000) =+68 09′ 47.76′′ ; van Leeuwen 2007), of spectral classifica-tion B2Ve (Guetter 1968). The position of HD200775 ismarked on Figure 2, although HD200775 itself is not vis-ible in the SCUBA-2 data.

L1172 lies to the south of L1174, and is also shown inFigure 2. It is forming stars much less actively than theneighbouring L1174.

L1147/L1158 contains the Lynds dark nebulae L1147,L1148, L1152, L1155, L1157, and L1158 (Lynds 1962). Thisregion is considered to be the least affected by the CFS,and to be forming stars with a low efficiency (K09). OnlyL1147, L1152, and L1155 were observed with SCUBA-2. Allof the emission seen in the western area shown in Figure 3is associated with L1152, except for the bright protostarL1157-mm and its associated outflow (Kun, Kiss & Balog2008), which are discussed below. All of the emission in theeastern region of Figure 3 is associated with L1155, with theexception of the bright point source in the north-east, thestar PV Cep (Li et al. 1994; discussed below).

Both L1152 and L1155 appear relatively quiescent(K09). There is some evidence that L1155 may be un-dergoing external heating: Nutter, Stamatellos & Ward-Thompson (2009) found evidence for a ∼ 2K temperaturegradient across one of the cores in the region, L1155C, whichthey ascribed to the effects of the nearby A6V star BD+671263 (marked on Figure 3).

The SCUBA-2 field contains two bright PMS stars:PV Cep (R.A. (J2000) = 20h 45m 53.943s , Dec. (J2000) =+67 57′ 38.66′′; Cutri et al. 2003) and L1157-mm(R.A. (J2000) = 20h 39m 06.2s, Dec. (J2000) = +6802′15′′;K09). PV Cep is a highly variable (Kun et al. 2009) A5Herbig Ae/Be star (Li et al. 1994), with which an extendedouflow is associated (Reipurth, Bally & Devine 1997). PVCep has a high westerly proper motion of ∼ 20 kms−1, andis likely to have escaped from the NGC7023 cluster, whichis discussed below (Goodman & Arce 2004). L1157-mm is aClass 0 protostar with an extremely strong molecular out-flow (Chini et al. 2001). The outflow is highly visible in the850-µm SCUBA-2 observations, and can be seen in Figures 3and 6, below.

L1251, shown in Figure 4, consists of threesubmillimetre-bright regions, the western L1251A, thecentral L1251C, and the eastern L1251E (Sato et al. 1994),surrounded by a network of filaments. L1251 appears to beactively forming stars; in particular, there is a small groupof young stars, L1251B, embedded within the L1251Eregion (Sato et al. 1994; Lee et al. 2007). K09 suggestthat star formation in L1251 may have been triggered orenhanced by the passage of the CFS ∼ 4Myr ago.

L1228, shown in Figure 5, is a small cloud which islikely to be located on the near side of the CFS, unlike theother clouds discussed here (Kun, Kiss & Balog 2008). L1228runs ∼ 3 along an approximately North-South axis. As canbe seen from the extinction contours in Figure 1, only thecentral part of L1228 was observed by the JCMT GBLS. K09note that L1228 is at a location consistent with the currentposition of the CFS, and suggest that star formation heremay be in the process of being enhanced by interaction withthe shell.

Enlargements of the regions of significant 850-µm emis-sion within each of the areas observed with SCUBA-2 areshown in Figure 6.

3.2 Source Extraction

We identified sources in the SCUBA-2 850-µm data usingCSAR (Cardiff Source-extraction AlgoRithm; Kirk et al.2013). CSAR is a dendrogram-based source-finding algo-rithm, which was run in its non-hierarchical mode. CSARidentifies a source based on a peak in the emission map andassigns neighbouring pixels to that source if those pixels areabove an assigned signal-to-noise criterion, and continues todo so until the contour level at which the source becomesconfused with its neighbours is reached.

We gridded each of the SCUBA-2 850-µm maps onto6-arcsec pixels before performing the source extraction. TheLR1 default pixel size is 3 arcsec at 850 µm. However, thebeam noise resulting from this oversampling of the data pre-vented CSAR from finding closed contours around extendedlow-surface-brightness sources. Source extraction was per-formed on the low-variance regions of the maps, where the

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6 K. Pattle et al.

Table 3. Sources identified in SCUBA-2 850-µm emission by CSAR and characterised using multiple-Gaussian fitting in the CepheusFlare region. FWHMs are as measured, without deconvolution. Position angles are measured east of north, and listed for elliptical sourcesonly. ‘Model’ peak and total flux density values are the results of the multiple-Gaussian fitting process, and are used in subsequent masscalculations. ‘Photometry’ peak and total flux density values are determined from aperture photometry, using the source sizes shownin Figure 6, and hence flux density will be double-counted in some of these measurements. ‘Photometry’ measurements are used in thesubsequent calculation of flux-ratio-determined temperature. 450-µm signal-to-noise is measured on peak value. Sources marked with ‘*’overlap significantly with at least one other source, listed in the final column. See text for details.

Model Photometry

Source RA Dec FWHM Angle Fpeakν(850)

Ftotalν(850)

Fpeakν(850)

Fpeakν(450)

Ftotalν(850)

Ftotalν(450)

450µm Type Region Overlaps

Index (J2000) (J2000) (arcsec) () (mJy/sqa) (Jy) (mJy/sqa) (Jy) S/N

1 20:39:05.28 68:02:20.40 21.6× 24.0 100.1 3.07 1.80 5.28 45.4 2.31 11.42 20.6 P 47/58 –2* 20:35:45.11 67:53:02.40 21.6× 26.4 5.4 0.83 0.54 1.23 10.8 0.98 5.72 4.9 P 47/58 33* 20:35:41.76 67:52:48.00 26.4× 26.4 – 0.78 0.62 1.17 10.8 1.14 5.88 4.9 C 47/58 24 20:35:54.72 67:54:10.80 57.8× 26.4 152.0 0.39 0.68 0.49 8.7 0.91 4.49 4.0 C 47/58 –5* 20:36:18.96 67:56:42.00 21.6× 21.6 – 0.10 0.05 0.40 7.7 0.08 0.87 3.5 P 47/58 206 20:45:53.28 67:57:39.60 23.4× 21.6 170.2 1.66 0.95 2.87 24.4 1.27 7.87 11.1 P 47/58 –7* 20:44:48.48 67:43:12.00 26.4× 26.4 – 0.16 0.13 0.35 8.0 0.42 2.49 3.6 C 47/58 88* 20:44:51.60 67:43:40.80 37.3× 26.4 125.0 0.14 0.15 0.35 8.0 0.51 2.73 3.6 C 47/58 7,109* 20:44:47.52 67:44:24.00 23.1× 26.4 43.0 0.12 0.08 0.31 7.4 0.26 0.79 3.4 C 47/58 1010* 20:44:50.88 67:44:13.20 26.4× 26.4 – 0.16 0.12 0.32 7.4 0.35 1.40 3.4 C 47/58 8,911* 20:36:10.80 67:57:14.40 21.6× 21.6 – 0.16 0.08 0.30 6.2 0.11 0.52 2.8 P 47/58 2012* 20:43:24.48 67:53:09.60 26.4× 25.7 170.0 0.07 0.06 0.32 7.2 0.24 0.77 3.3 C 47/58 1813* 20:43:10.56 67:51:00.00 26.4× 24.3 10.0 0.10 0.07 0.27 7.3 0.23 0.39 3.3 C 47/58 1414* 20:43:18.24 67:50:56.40 21.6× 26.4 37.5 0.10 0.06 0.27 7.9 0.2 1.25 3.6 C 47/58 1315 20:43:49.20 67:51:00.00 21.6× 26.4 173.0 0.09 0.06 0.27 7.6 0.16 0.75 3.4 C 47/58 –16* 20:38:06.96 67:55:30.00 26.4× 21.6 80.0 0.06 0.04 0.26 6.1 0.19 0.28 2.8 C 47/58 1917* 20:43:25.68 67:52:22.80 21.6× 21.6 177.0 0.08 0.04 0.30 8.2 0.17 0.94 3.7 C 47/58 1818* 20:43:29.76 67:52:55.20 66.4× 29.8 121.7 0.13 0.30 0.32 8.2 0.68 3.36 3.7 C 47/58 12,1719* 20:38:04.57 67:55:51.60 21.6× 26.4 0.0 0.04 0.02 0.26 6.3 0.19 0.44 2.9 C 47/58 1620* 20:36:05.76 67:56:45.60 72.2× 26.4 19.6 0.20 0.43 0.29 7.6 0.48 2.35 3.4 C 47/58 5,1121 21:01:40.81 68:12:03.60 26.4× 23.7 10.0 1.33 0.94 2.03 18.4 1.94 16.91 18.4 C L1174 –22* 21:00:19.68 68:13:22.80 22.8× 26.4 100.0 0.76 0.52 1.98 14.6 1.47 8.07 14.6 P L1174 25,2623* 21:01:28.80 68:10:33.60 29.8× 26.4 147.2 1.61 1.43 1.77 19.0 2.14 18.08 19.0 P L1174 2424* 21:01:30.96 68:11:20.40 31.2× 25 112.8 1.47 1.30 1.61 17.3 2.20 19.26 17.3 P L1174 2325* 21:00:23.04 68:13:12.00 26.4× 26.4 – 1.17 0.93 1.98 14.6 1.72 10.83 14.6 P L1174 22,2626* 21:00:17.28 68:12:46.80 26.4× 26.4 – 0.99 0.78 1.12 7.2 1.36 7.33 7.2 C L1174 22,2527* 21:02:13.92 68:09:14.40 57.2× 26.4 127.9 0.62 1.05 0.70 7.3 1.48 11.64 7.3 C L1174 2828* 21:02:11.04 68:09:54.00 21.6× 26.4 10.0 0.20 0.13 0.47 5.6 0.46 3.58 5.6 C L1174 2729* 21:01:28.32 68:08:20.40 26.4× 24.6 71.8 0.24 0.18 0.41 4.8 0.44 2.71 4.8 C L1174 35,4130* 21:03:20.16 68:11:31.20 26.4× 26.4 – 0.12 0.10 0.52 3.7 0.50 1.96 3.7 C L1174 3131* 21:03:15.12 68:11:16.80 30.8× 26.4 115.8 0.17 0.15 0.52 3.2 0.55 1.49 3.2 C L1174 30

32 20:59:22.56 68:14:49.20 22.3× 21.6 10.0 0.18 0.10 0.39 3.2 0.15 0.22 3.2 P L1174 –33* 21:02:00.72 68:07:12.00 26.4× 21.6 172.8 0.10 0.06 0.36 3.4 0.29 0.68 3.4 C L1174 3934 21:01:31.20 68:07:19.20 42.3× 21.9 24.4 0.26 0.27 0.48 5.2 0.73 4.69 5.2 C L1174 –35* 21:01:34.32 68:08:16.80 21.6× 26.4 0.0 0.07 0.04 0.40 4.2 0.34 1.69 4.2 P L1174 29,4136 21:01:31.20 68:05:38.40 24× 24 – 0.22 0.15 0.35 3.8 0.25 1.44 3.8 C L1174 –37 21:02:48.72 68:11:45.60 24.9× 26.4 10.0 0.10 0.08 0.34 2.7 0.30 0.81 2.7 C L1174 –38 21:00:28.56 68:07:08.40 45.5× 26.4 40.3 0.25 0.34 0.43 4.7 0.78 3.55 4.7 C L1174 –39* 21:01:56.39 68:06:39.60 46.1× 26.4 136.3 0.22 0.30 0.40 3.1 0.74 2.37 3.1 C L1174 3340 21:02:00.96 68:13:01.20 73.6× 46 122.7 0.22 0.86 0.41 4.3 1.61 6.08 4.3 C L1174 –41* 21:01:32.64 68:08:38.40 26.4× 21.6 161.8 0.23 0.15 0.41 4.2 0.33 1.96 4.2 P L1174 29,3542 21:00:24.25 68:14:06.00 26.4× 21.6 95.6 0.10 0.07 0.37 3.9 0.26 0.38 3.9 C L1174 –43 21:00:37.92 68:06:18.00 21.6× 26.4 1.4 0.14 0.09 0.31 4.1 0.27 0.74 4.1 C L1174 –44 21:00:23.52 68:08:13.20 38× 26.4 148.7 0.18 0.20 0.40 4.1 0.57 2.61 4.1 C L1174 –45 21:02:09.12 68:07:08.40 25.6× 26.4 170.0 0.15 0.11 0.39 3.6 0.36 1.46 3.6 C L1174 –46 21:02:39.60 68:11:24.00 27× 26.4 175.2 0.17 0.14 0.38 3.5 0.41 0.70 3.5 C L1174 –47* 21:02:20.64 67:54:21.60 23.5× 26.4 177.6 0.41 0.29 0.72 8.4 0.70 3.72 3.8 P L1172 4848* 21:02:26.40 67:54:14.40 26.4× 24 170.0 0.38 0.28 0.65 7.1 0.65 3.27 3.2 P L1172 4749 21:02:13.20 67:54:03.60 22.3× 26.4 80.0 0.10 0.07 0.36 5.9 0.35 1.49 2.7 C L1172 –50 21:02:20.64 67:45:36.00 21.6× 26.4 170.0 0.09 0.06 0.27 8.0 0.18 1.14 3.7 C L1172 –51* 21:01:51.60 67:44:06.00 23.8× 26.4 170.0 0.08 0.05 0.24 7.5 0.20 0.72 3.4 C L1172 5352 21:02:15.84 67:51:10.80 29.5× 21.6 53.4 0.10 0.07 0.26 6.1 0.21 1.00 2.8 C L1172 –53* 21:01:52.08 67:43:40.80 26.4× 25.7 10.0 0.08 0.06 0.24 7.5 0.21 0.61 3.4 C L1172 5154 21:02:29.76 67:53:24.00 21.6× 26.4 170.0 0.07 0.05 0.24 5.6 0.16 0.31 2.5 C L1172 –55 21:02:41.28 67:54:10.80 33× 26.4 84.7 0.17 0.17 0.26 5.3 0.19 0.55 2.4 C L1172 –56* 22:38:47.04 75:11:31.20 33.4× 23.8 9.9 3.54 3.19 4.22 34.9 3.67 23.33 19.7 P L1251 58,59

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First SCUBA-2 observations of Cepheus 7

Table 3. – continued.

Model Photometry

Source RA Dec FWHM Angle Fpeakν(850)

Ftotalν(850)

Fpeakν(850)

Fpeakν(450)

Ftotalν(850)

Ftotalν(450)

450µm Type Region Overlaps

Index (J2000) (J2000) (arcsec) () (mJy/sqa) (Jy) (mJy/sqa) (Jy) S/N

57* 22:31:04.32 75:13:37.20 53.7× 26.4 27.2 0.92 1.48 1.02 7.2 1.57 7.71 7.7 P L1251 62,6358* 22:39:04.56 75:12:00.00 26.4× 26.4 – 0.76 0.60 0.70 8.4 0.98 3.47 4.8 C L1251 5959* 22:38:56.16 75:11:42.00 26.4× 24.3 177.6 0.65 0.47 3.50 28.9 1.08 5.37 16.3 C L1251 56,5860* 22:39:38.40 75:12:03.60 53.3× 39.0 93.2 0.80 1.89 0.92 6.6 2.51 7.00 3.7 C L1251 6461 22:35:22.56 75:17:06.00 27.1× 25.3 80.0 1.89 1.47 2.81 23.0 2.18 14.62 13.0 P L1251 –62* 22:31:12.48 75:12:57.60 26.4× 26.4 – 0.34 0.27 0.69 4.5 0.66 3.50 4.8 C L1251 57,6363* 22:31:22.08 75:12:28.80 65.7× 26.4 19.9 0.41 0.81 0.45 4.5 1.03 6.41 4.8 C L1251 57,6264* 22:39:30.00 75:10:58.80 28.7× 24.4 158.9 0.58 0.46 0.73 6.4 0.80 2.61 3.6 C L1251 6065 22:39:16.08 75:09:43.20 32.3× 25.6 49.5 0.19 0.18 0.35 5.1 0.31 0.51 2.9 C L1251 –66* 22:28:15.36 75:14:38.40 40.6× 23.4 146.6 0.42 0.45 0.45 3.8 0.58 2.40 4.1 C L1251 6767* 22:28:24.72 75:14:56.40 26.4× 21.6 170.0 0.15 0.10 0.39 3.5 0.30 1.36 3.8 C L1251 6668* 22:35:52.32 75:18:57.60 41.0× 24.5 109.8 0.39 0.45 0.51 8.3 0.66 3.78 4.7 C L1251 8669 22:34:39.84 75:17:49.20 21.6× 21.6 – 0.14 0.08 0.27 4.2 0.08 0.74 2.4 P L1251 –70* 22:35:34.08 75:21:18.00 21.6× 26.4 172.3 0.11 0.07 0.31 5.0 0.24 0.78 2.8 C L1251 87,8871 22:29:41.52 75:13:30.00 42.6× 32.1 15.0 0.66 1.02 0.75 5.7 1.32 7.10 6.1 C L1251 –72 22:39:13.20 75:10:44.40 30.4× 26.4 163.5 0.18 0.17 0.36 6.4 0.33 1.08 3.6 C L1251 –73 22:36:40.80 75:08:31.20 26.4× 23.8 10.0 0.08 0.06 0.26 7.0 0.21 1.07 4.0 C L1251 –74 22:35:04.80 75:13:01.20 27.7× 26.4 29.7 0.14 0.12 0.27 5.2 0.29 2.19 2.9 C L1251 –75* 22:39:24.24 75:12:39.60 26.4× 26.4 – 0.15 0.12 0.32 6.1 0.28 -0.17 3.4 C L1251 –76 22:34:10.80 75:18:10.80 21.6× 21.6 – 0.14 0.07 0.26 4.7 0.12 0.31 2.7 P L1251 9377* 22:35:59.76 75:07:48.00 26.4× 26.4 – 0.09 0.07 0.25 4.9 0.27 0.30 2.8 C L1251 –78* 22:27:31.44 75:11:24.00 36.1× 25.8 143.7 0.16 0.17 0.31 2.9 0.36 1.62 3.1 C L1251 7979* 22:36:07.20 75:07:58.80 25.7× 26.4 0.0 0.08 0.06 0.24 5.5 0.23 0.06 3.1 C L1251 83,85,8980 22:38:21.60 75:13:01.20 31.8× 21.6 39.1 0.16 0.13 0.26 6.0 0.18 1.32 3.4 C L1251 7781 22:37:00.00 75:15:21.60 26.4× 21.6 96.8 0.09 0.06 0.28 4.9 0.21 0.24 2.8 C L1251 –82 22:30:30.72 75:14:13.20 29.2× 25.8 146.8 1.04 0.88 1.41 12.8 1.13 5.79 13.7 P L1251 –83* 22:27:37.69 75:12:14.40 23.1× 21.6 10.0 0.10 0.06 0.31 2.9 0.18 0.90 3.1 C L1251 –84 22:35:20.64 75:18:57.60 27.3× 21.6 65.4 0.32 0.21 0.42 6.7 0.33 2.29 3.8 P L1251 78,85,8985* 22:27:31.68 75:12:07.20 26.4× 26.4 8.4 0.06 0.05 0.31 2.9 0.25 1.07 3.1 C L1251 –86* 22:35:42.00 75:18:54.00 26.4× 24.9 10.0 0.14 0.10 0.35 6.6 0.25 1.69 3.8 C L1251 78,83,89

87* 22:35:31.44 75:21:54.00 22.1× 26.4 10.0 0.09 0.06 0.28 4.7 0.25 0.92 2.7 C L1251 6888* 22:35:38.88 75:21:25.20 47.6× 21.6 64.1 0.08 0.09 0.31 5.3 0.42 1.63 3.0 C L1251 70,8889* 22:27:38.87 75:11:45.60 33.3× 26.4 3.3 0.10 0.10 0.31 3.3 0.31 1.69 3.5 C L1251 70,8790 22:37:44.16 75:09:43.20 35.8× 26.4 129.3 0.16 0.17 0.27 5.5 0.28 0.20 3.1 C L1251 78,83,8591 22:29:59.76 75:13:55.20 38.1× 26.4 73.9 0.20 0.23 0.35 4.3 0.49 3.50 4.6 P L1251 –92 22:38:44.40 75:14:02.40 26.4× 21.6 18.2 0.13 0.08 0.26 6.7 0.18 0.73 3.8 C L1251 –93* 22:39:17.52 75:13:44.40 71.2× 27.5 77.1 0.42 0.94 0.50 7.5 0.85 0.66 4.2 C L1251 7594* 22:37:08.88 75:08:49.20 26.4× 26.4 – 0.10 0.08 0.28 5.5 0.30 1.13 3.1 C L1251 9795 22:37:34.57 75:11:34.80 65.6× 38.3 134.0 0.38 1.07 0.46 6.4 1.50 5.33 3.6 C L1251 –96 22:36:18.72 75:22:15.60 50.3× 27.2 130.8 0.22 0.34 0.35 5.3 0.56 0.30 3.0 C L1251 –97* 22:37:00.71 75:08:42.00 33.7× 26.4 114.4 0.11 0.11 0.27 5.7 0.37 1.76 3.2 C L1251 9498 20:58:02.16 77:33:18.00 33.7× 31.2 126.0 0.24 0.28 0.34 3.1 0.52 2.00 3.5 C L1228 –99 20:57:18.24 77:37:51.60 24.0× 24.0 – 0.20 0.13 0.27 3.9 0.23 1.32 4.4 C L1228 –

100* 20:56:41.28 77:41:24.00 42.7× 30.0 15.8 0.18 0.26 0.30 3.5 0.60 2.16 3.9 C L1228 104101 20:55:54.24 77:42:46.80 44.5× 26.4 18.2 0.19 0.25 0.31 3.2 0.48 1.86 3.6 C L1228 –102 20:57:13.68 77:44:06.00 26.4× 21.6 35.0 0.11 0.07 0.26 3.5 0.20 1.00 3.9 C L1228 –103 20:54:49.44 77:32:24.00 26.4× 21.6 170.0 0.12 0.07 0.23 2.3 0.15 0.36 2.6 C L1228 –104* 20:56:42.24 77:40:55.20 26.4× 26.4 – 0.12 0.09 0.29 3.5 0.32 1.11 3.9 C L1228 100105 20:54:59.04 77:50:34.80 21.6× 21.6 – 0.04 0.02 0.24 3.1 0.14 0.52 3.5 C L1228 –106 20:57:39.60 77:43:37.20 62.8× 40.7 175.2 0.36 1.03 0.53 4.4 1.33 5.85 4.9 C L1228 –107 20:57:47.76 77:37:19.20 30.0× 26.5 147.4 0.17 0.15 0.30 2.5 0.31 0.64 2.8 C L1228 –108* 20:56:27.37 77:24:43.20 35.2× 26.4 118.4 0.07 0.07 0.26 2.8 0.29 0.29 3.1 C L1228 115109 20:58:49.68 77:47:16.80 26.2× 21.6 100.0 0.07 0.04 0.21 2.7 0.19 0.30 3.0 C L1228 –110 20:55:11.28 77:33:21.60 21.8× 21.6 55.0 0.09 0.05 0.24 2.7 0.16 0.28 3.0 C L1228 –111 20:57:12.24 77:35:45.60 26.4× 21.8 100.5 2.20 1.43 3.65 29.0 2.03 9.00 32.2 P L1228 –112 20:55:18.48 77:45:46.80 25.1× 21.6 0.5 0.06 0.04 0.31 3.3 0.21 1.04 3.7 C L1228 –113* 20:58:19.92 77:42:36.00 37.4× 25.9 35.0 0.11 0.12 0.25 3.2 0.32 1.42 3.5 C L1228 116114 20:54:49.44 77:43:33.60 21.6× 24.6 173.7 0.08 0.05 0.22 2.7 0.13 0.33 3.0 C L1228 –115* 20:56:18.00 77:24:57.60 34.6× 26.4 142.4 0.16 0.17 0.28 2.6 0.38 0.51 2.9 C L1228 108116* 20:58:30.24 77:42:43.20 26.4× 21.6 3.0 0.11 0.07 0.25 3.2 0.19 1.01 3.5 C L1228 113117 20:57:17.05 77:33:21.60 31.9× 24.1 129.7 0.13 0.11 0.26 2.6 0.28 0.75 2.9 C L1228 –

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Figure 4. SCUBA-2 850-µm observations of the L1251 region, with sources marked. The ellipses show twice the FWHM size of eachsource. Contours of Av of 0.5, 1.0, 1.5 and 2.0 magnitudes are shown for reference (Dobashi et al. 2005). The dashed lines markapproximately the boundaries between the L1251A, L1251C and L1251E regions. The protostellar cluster L1251B is labelled.

Figure 5. SCUBA-2 850-µm observations of the L1228 region,with sources marked. The ellipses show twice the FWHM size ofeach source. Contours of Av of 0.5, 1.0, 1.5 and 2.0 magnitudes areshown for reference (Dobashi et al. 2005). The protostar L1228 islabelled.

variance, as measured in the variance array, was very low,< 0.005 (mJy/arcsec2)2. The criteria chosen for a robustly-detected source were a peak flux density F peak

ν > 5 σ anda minimum of a 1 σ drop in flux density between adjacent

sources (i.e. a local minimum in flux density at least 1σ lessthan peak value of the fainter of the two sources), whereσ is the RMS noise level of the data. We adopted 1σ val-ues of 0.041 mJy/arcsec2 in L1174, and 0.028 mJy/arcsec2

elsewhere on 6-arcsec pixels at 850 µm.

We identified 27 sources in L1147/58, 26 sources inL1174, 9 sources in L1172, 42 sources in L1251 and 20sources in L1228. Of the 27 sources in L1147/58, 7 were re-jected due to their being associated with the L1157-mm out-flow and hence likely to be artefacts resulting from CO con-tamination in the SCUBA-2 850-µm data. Rejecting theseleft us with 20 reliable sources in L1147/58. There were nosources in other regions which we considered likely to be COartefacts.

The sources we identified in each cloud are shown indetail on Figure 6, and on Figures 3–5 for reference. Dueto the significant overlap between some of the sources, wefitted each source using a multiple-Gaussian fitting routine.This model, which utilises the fitting routine mpfit (Mark-wardt 2009), is described in detail by Pattle et al. (2015).The fitting routine models the flux density of sources incrowded regions by fitting a two-dimensional Gaussian andan inclined-plane background to each of a set of associatedsources simultaneously. Sources are considered to be neigh-bours if they are separated by less than twice the FWHMof the larger source. Groups to be fitted simultaneously aredefined such that each source in a group is a neighbour to atleast one other source in the group, and no source has anyneighbours outside of the group. The source positions andsizes determined using CSAR were supplied as initial input

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First SCUBA-2 observations of Cepheus 9

Figure 6. SCUBA-2 850-µm observations of regions of significant emission. Sources extracted in this work are numbered as in Table 3and colour-coded by region: red – L1147/58; light green – L1172; dark green – L1174; blue – L1251; purple – L1228. The data are shownin square-root scaling.

to the fitting routine. The Gaussian fitting routine was con-strained such that for each source, the x and y coordinatesof the source could vary no more than 6 arcsec from theirinitial position, the source semi-major and semi-minor axescould not vary by more than 10 per cent of their initial val-ues, and the source position angle could vary by no morethan 5. The total flux of the source was constrained to bepositive.

It should be noted that while the Gaussian model isa popular and widely-used choice of model for characteris-

ing the properties of starless cores (e.g. Ward-Thompsonet al. 1994; Hirota, Ito & Yamamoto 2002; Enoch et al.2008; Gomez et al. 2014; Pattle et al. 2015), the underly-ing geometry of a starless core is unlikely to obey a Gaus-sian distribution, instead typically showing a flat centralplateau and power-law wings (e.g. Alves, Lada & Lada2001), which may be characterised using a Bonnor-Ebertgeometry (Ebert 1955; Bonnor 1956) or a Plummer-like ge-ometry (Plummer 1911; Whitworth et al. 1996). However,the Gaussian model remains a very useful tool for character-

c© 2016 RAS, MNRAS 000, 1–29

10 K. Pattle et al.

Table 4. The protostellar sources in our catalogue, with their identification and evolutionary class from K09, and alternative identifica-tions. With the exception of L1157-mm and stars with an identification of the form XX Cep, alternative identifications are given in thefollowing order of preference: IRAS Point or Faint Source Catalogs (IRAS – Beichman et al. 1988; Moshir, Kopman & Conrow 1992),2MASS All-Sky Catalog of Point Sources (2MASS – Cutri et al. 2003), Spitzer Gould Belt Survey (SSTgbs – K09). For the L1251Bcluster, designations from Lee et al. (2006) are also given. K09 identifications given in brackets indicate an offset between our sourcecentral coordinates and the coordinates of the K09 source greater than the JCMT 850-µm beam size, but less than the radius of thesource as listed in Table 3.

Source ID K09 ID K09 Class Alternative ID

1 134 I L1157-mm2 1 I IRAS 20353+67425 3 II IRAS 20359+64756 135 I PV Cep11 2 II 2MASS J2036+1165+675709322 17 I SSTgbs J2100207+6813169

22 (100) F SSTgbs J2100224+681304223 27 II 2MASS J21012637+681038523 137 II SSTgbs J2101271+681038024 34 I 2MASS J21013280+681120425 18 I SSTgbs J2100221+681258525 (100) F SSTgbs J2100224+681304232 15 II FT Cep35 (104) F PW Cep41 (104) F PW Cep47 49 I IRAS 21017+674248 50 F SSTgbs J2102273+675418648 (53) II 2MASS J21022993+675408356 89 I 2MASS J22384282+7511369; L1251B IRS 456 90 I SSTgbs J2238469+7511337; L1251B IRS 156 92 I 2MASS J22385287+7511235; L1251B IRS 256 107 III IRAS 22376+7455; L1251B IRS 356 108 III SSTgbs J2238440+7511266; L1251B IRS 556 109 II 2MASS J22384807+7511488; L1251B IRS 657 68 II SSTgbs J2231056+751337261 143 I IRAS 22343+750169 69 F 2MASS J22344051+751744476 142 F IRAS 22331+750282 67 I SSTgbs J2230318+751409484 (76) II 2MASS J22351668+751847191 66 I IRAS 22290+7458111 9 F IRAS 20582+7724; L1228

ising the properties of ensembles of starless cores, due to itsanalytic tractability. Gaussian fits may underestimate coresize (Terebey, Chandler & Andre 1993), typically fitting thecentral plateau of the core and underestimating the extentof the wings. However, two arguments mitigate against theeffect of this on our core sample. Firstly, if we were signifi-cantly underestimating the size of our cores, then we wouldexpect to see positive annuli of unfitted flux in the resid-uals of our Gaussian fits, which is not the case. Secondly,it can be shown that for Gaussian and Plummer-like distri-butions with the same total mass and central density, thecharacteristic sizes of the two distributions are very similar,RPlummer = 1.17RGaussian, where RPlummer is the charac-teristic size of the Plummer-like distribution and RGaussian

is the Gaussian width (assuming a power-law index for thePlummer-like distribution of 4; see Pattle 2016 for deriva-tions of the masses of the two distributions). This suggeststhat we are unlikely to be significantly underestimating thesize of our cores by using a Gaussian distribution.

In this analysis we are concerned with the ensembleproperties of starless cores in the Cepheus molecular cloud,and so require an approximate size and mass estimate foreach core, which can be usefully provided by a Gaussian fit

to the data. Future detailed analyses of the interior struc-ture of starless cores using SCUBA-2 data will require moresophisticated modelling of core geometries.

For each of our sources, Table 3 lists the position, angu-lar size, orientation, peak and total flux densities, signal-to-noise ratio at 450 µm, classification as starless or protostel-lar, and the region in which the source is located. For the850-µm flux densities, both the modelled values and the val-ues determined from aperture photometry are listed. For the450-µm flux densities, only values determined from aperturephotometry are listed. The aperture photometry measure-ments were made using elliptical apertures with major andminor axis diameters of twice the FWHM values listed inTable 3, and as shown in Figures 3–6.

Prior to aperture photometry measurements beingmade, the 450-µm data were convolved to match the res-olution of the 850-µm data using a convolution kernel con-structed as described by Pattle et al. (2015), following themethod proposed by Aniano et al. (2011). The convolutionkernel used was constructed using the SCUBA-2 450-µmand 850-µm beam models given by Dempsey et al. (2013).However, the peak 450-µm flux densities, and the 450-µm

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First SCUBA-2 observations of Cepheus 11

signal-to-noise ratios, were determined from the original,non-convolved map.

We emphasise that due to the significant overlap be-tween many of the sources (see Figures 3–5), there will bedouble-counting of pixels in many of the flux densities deter-mined from aperture photometry, and the flux density valuesdetermined from aperture photometry are likely to be over-estimates of the amount of emission associated with a source.The aperture-photometry-determined peak flux densities arethose of the brightest pixel in the source aperture, and somay be identical for overlapping sources. The modelling-determined peak flux densities are the best-fit peak fluxdensities assuming the sources obey Gaussian distributions.

It can be seen in Table 3 that the aperture-photometry-determined 850-µm flux densities are typically ∼ 30 per centhigher than the model 850-µm flux densities in isolated (non-overlapping) sources. This is due to the inclined-plane back-ground which is fitted to the measured emission along withthe Gaussian source model.

Note that the 450-µm and 850-µm aperture-photometry-determined flux densities do not have theSCUBA-2 aperture photometry corrections discussed byDempsey et al. (2013) applied to them. The SCUBA-2aperture photometry corrections are determined for pointsources, and account for flux in the secondary beam ofthe JCMT not enclosed by a small aperture (the JCMT’ssecondary beam has a FWHM of 25 arcsec at 450µm and48 arcsec at 850 µm; see Dempsey et al. 2013) . We do notuse these aperture photometry corrections in this work,as their applicability to either extended sources or non-circular apertures is not certain. Furthermore, for aperturediameters from 25 to 50 arcsec (i.e. the vast majority ofour sources), the 450-µm and 850-µm aperture photometrycorrections are identical, while for sources larger than 50arcsec, the difference between the 450-µm and 850-µmcorrections is very small, typically ∼ 1 per cent (Dempseyet al. 2013). As we are using the aperture-photometry-determined flux densities only as a ratio quantity (see3.4, below), use of the aperture photometry corrections(or otherwise) should not affect our results. However, asaperture-photometry-corrected flux densities may be usefulfor other purposes, we direct the reader to Dempsey et al.(2013) for further information.

In the analysis that follows, we use the best-fit model850-µm total flux densities in order to determine sourcemasses. The ratio of the 450-µm and 850-µm aperture-photometry-determined total flux densities are used to de-termine source temperatures, for those sources with a peak450-µm signal-to-noise ratio > 3 – see Section 3.4 below.

3.3 Source Characterisation

Of the 117 sources in our Cepheus Flare catalogue, 23 wereassociated with at least one protostar in the K09 Spitzercatalogue. (The K09 catalogue lists 143 protostellar sourcesand covers all of the regions observed with SCUBA-2.) Pro-tostar associations are listed in Table 4, along with the K09source with which they are associated, the evolutionary classof that source (as determined from the infrared spectral in-dex, αir by K09), and alternative identifications. It shouldbe noted that due to the ∼ 300 pc distances to the CepheusFlare clouds, a single SCUBA-2 source in Cepheus may be

associated with more than one protostellar object. In partic-ular, source 56 contains six embedded sources, the L1251Bgroup.

The K09 Spitzer catalogue is the only systematic pro-tostar catalogue produced from Spitzer observations ofCepheus to date. We compared the K09 results to a morelimited recent study by Dunham et al. (2013), who revisethe classification of a number of protostars detected by theSpitzer c2d (Evans et al. 2009) and Gould Belt (P.I. L. Allen;see, e.g., K09) surveys. Dunham et al. (2013) extend themethods developed by Evans et al. (2009) for correctingprotostellar fluxes and luminosities for extinction, provid-ing corrected classifications for Spitzer -detected protostarsassociated with at least one submillimetre detection at wave-lengths > 350µm. Dunham et al. (2013) include 20 proto-stars in Cepheus in their sample, all of which are includedin the K09 catalogue. The Dunham et al. (2013) extinctioncorrections alter the αir classification of two of the 20 starswhich they consider in Cepheus, both of which we detectwith SCUBA-2: Source 48 (K09 Source 50), which is re-classified from Flat to Class II, and Source 91 (K09 Source66), which is reclassified from Class I to Flat. Source 111(K09 source 9) also moves from Class I to the Class I/Flatboundary. As these extinction-corrected classifications areavailable for only a subset of the Spitzer sources in Cepheus,and as only a small minority of the source classifications arechanged by the correction for extinction, we continue to usethe classifications given in K09 throughout this work. This isin order to use a self-consistent set of source classifications.

Temperatures for each of our sources were supplied byDi Francesco et al. (2016, in prep.). These temperatures weredetermined from SED fitting to the 160–500-µm Herschel

observations taken toward the Cepheus Flare as part of theHerschel Gould Belt Survey (GBS) (Andre et al. 2007). TheHerschel data were fitted by Di Francesco et al. (2016, inprep.) using the model

Fν =MBν(T )κν

D2, (1)

where Fν is the measured flux density, Bν(T ) is the Planckfunction, M is the source mass, D is the distance to thesource, and the Beckwith et al. (1990) parameterisation ofdust opacity, κν = 0.1(ν/1012Hz)β cm2g−1, is used, assum-ing a dust emissivity index β = 2.0. We use this model fordust opacity and this value of dust emissivity index through-out the rest of this work, in order to combine the Herschel

data with our own in a self-consistent manner. This model ofdust properties, adopted by the Herschel GBS, is describedin detail by, e.g., Konyves et al. (2015).

We note that combined SCUBA-2 and Herschel ob-servations have demonstrated variations in β toward star-forming regions in the range β = 1.6 − 2.0 (Sadavoy et al.2013) and β = 1.0−2.7 (Chen et al. 2016), with lower valuesof β typically observed toward protostellar cores. Sadavoyet al. (2013) found β ≈ 2.0 toward filaments and moderatelydense material, suggesting that β = 2.0 is a representativevalue for the starless cores in our sample, but may be lessappropriate for the protostellar sources which we observe.

The SED fitting process is described in detail byKonyves et al. (2015). It must be emphasised that the onlyquantity derived from the Herschel data which we use isthe source temperature. We discuss our own determinations

c© 2016 RAS, MNRAS 000, 1–29

12 K. Pattle et al.

Table 5. Properties of the sources. See text for discussion.

Source THerschel TSCUBA-2 M(THerschel) M(TSCUBA-2) N(H2) n(H2) Deconv.Index (K) (K) (M⊙) (M⊙) (×1021 cm−2) (×104 cm−3) FWHM (pc)

1 14.8± 0.2 10.7± 1.7 2.43± 0.07 4.36± 1.35 42.66± 1.30 36.81± 1.12 0.0282 12.4± 0.3 – 0.99± 0.05 – 14.91± 0.80 11.93± 0.64 0.0303 11.5± 0.2 – 1.31± 0.06 – 14.77± 0.66 10.21± 0.45 0.0354 10.6± 0.1 – 1.70± 0.07 – 7.17± 0.31 3.03± 0.13 0.0575 13.1± 0.2 – 0.08± 0.01 – 1.78± 0.30 1.68± 0.28 0.0266 16.2± 0.2 13.5± 2.8 1.11± 0.03 1.51± 0.55 20.19± 0.58 17.75± 0.51 0.0287 11.7± 0.0 – 0.26± 0.02 – 2.93± 0.19 2.02± 0.13 0.0358 11.5± 0.1 – 0.32± 0.02 – 2.29± 0.16 1.26± 0.09 0.0449 11.7± 0.1 – 0.17± 0.02 – 2.31± 0.25 1.76± 0.19 0.03210 11.5± 0.1 – 0.26± 0.02 – 2.93± 0.21 2.02± 0.14 0.03511 12.3± 0.0 – 0.15± 0.01 – 3.21± 0.30 3.03± 0.28 0.02612 11.5± 0.1 – 0.12± 0.02 – 1.36± 0.19 0.96± 0.14 0.03513 11.5± 0.0 – 0.15± 0.02 – 1.94± 0.21 1.42± 0.15 0.03314 11.6± 0.0 – 0.13± 0.02 – 1.95± 0.24 1.56± 0.19 0.03015 12.4± 0.0 – 0.11± 0.01 – 1.64± 0.20 1.32± 0.16 0.03016 13.3± 0.1 – 0.06± 0.01 – 0.94± 0.18 0.75± 0.15 0.03017 11.5± 0.1 – 0.09± 0.02 – 1.79± 0.33 1.68± 0.31 0.02618 11.3± 0.1 – 0.65± 0.03 – 2.05± 0.11 0.75± 0.04 0.06619 13.2± 0.0 – 0.04± 0.01 – 0.57± 0.18 0.45± 0.14 0.03020 11.5± 0.1 – 0.91± 0.04 – 2.99± 0.14 1.12± 0.05 0.06521 16.7± 0.5 23.3± 9.6 0.82± 0.05 0.50± 0.29 13.68± 0.86 11.52± 0.72 0.02922 13.1± 0.1 11.9± 2.1 0.68± 0.02 0.81± 0.27 12.00± 0.39 10.40± 0.34 0.02823 27.6± 1.5 21.8± 8.2 0.60± 0.05 0.83± 0.45 7.31± 0.58 5.25± 0.42 0.03424 19.2± 1.1 23.5± 9.8 0.91± 0.08 0.68± 0.40 11.17± 1.04 8.07± 0.75 0.03425 13.2± 0.1 13.7± 2.9 1.19± 0.03 1.12± 0.41 17.06± 0.41 13.30± 0.32 0.03126 11.9± 0.3 11.6± 2.0 1.21± 0.07 1.27± 0.42 17.40± 0.94 13.57± 0.73 0.03127 20.3± 1.4 18.9± 6.0 0.68± 0.08 0.75± 0.36 3.70± 0.42 1.78± 0.20 0.05128 21.8± 0.6 18.7± 6.0 0.08± 0.01 0.09± 0.05 1.45± 0.17 1.31± 0.15 0.02729 26.9± 1.1 – 0.08± 0.01 – 1.22± 0.14 1.00± 0.11 0.03030 15.5± 0.2 – 0.09± 0.01 – 1.36± 0.17 1.06± 0.13 0.03131 15.1± 0.2 – 0.16± 0.02 – 1.81± 0.18 1.27± 0.13 0.03532 14.1± 0.1 – 0.11± 0.01 – 2.87± 0.33 2.97± 0.34 0.02433 25.3± 0.3 – 0.03± 0.01 – 0.57± 0.10 0.51± 0.09 0.02734 19.5± 0.4 14.0± 3.1 0.18± 0.02 0.32± 0.12 1.81± 0.15 1.17± 0.10 0.03835 28.4± 1.2 – 0.02± 0.01 – 0.34± 0.10 0.31± 0.09 0.02736 18.2± 0.4 – 0.11± 0.01 – 2.09± 0.22 1.87± 0.20 0.02737 15.5± 0.0 – 0.07± 0.01 – 1.16± 0.16 0.94± 0.13 0.03038 19.5± 0.7 – 0.23± 0.02 – 1.67± 0.16 0.92± 0.09 0.04439 24.2± 0.6 – 0.15± 0.01 – 1.07± 0.09 0.58± 0.05 0.04540 18.8± 1.3 – 0.62± 0.08 – 1.38± 0.18 0.43± 0.06 0.07941 31.0± 1.1 – 0.05± 0.01 – 1.01± 0.12 0.91± 0.11 0.02742 13.2± 0.1 – 0.08± 0.01 – 1.61± 0.27 1.45± 0.25 0.02743 21.2± 0.3 – 0.05± 0.01 – 1.02± 0.14 0.92± 0.13 0.027

44 18.9± 0.5 – 0.15± 0.01 – 1.30± 0.13 0.80± 0.08 0.04045 23.6± 0.5 – 0.06± 0.01 – 0.88± 0.11 0.70± 0.09 0.03146 16.3± 0.3 – 0.12± 0.01 – 1.69± 0.17 1.29± 0.13 0.03247 12.0± 0.0 – 0.45± 0.01 – 7.56± 0.21 6.40± 0.18 0.02948 12.1± 0.1 – 0.42± 0.02 – 6.81± 0.28 5.68± 0.23 0.02949 11.8± 0.1 – 0.10± 0.01 – 1.91± 0.23 1.69± 0.20 0.02850 12.9± 0.0 – 0.07± 0.01 – 1.42± 0.19 1.29± 0.17 0.02751 12.7± 0.1 – 0.08± 0.01 – 1.27± 0.18 1.06± 0.15 0.02952 12.5± 0.0 – 0.10± 0.01 – 1.61± 0.19 1.34± 0.15 0.02953 12.6± 0.1 – 0.08± 0.01 – 1.20± 0.16 0.95± 0.13 0.03154 12.3± 0.1 – 0.07± 0.01 – 1.33± 0.22 1.20± 0.20 0.02755 12.5± 0.1 – 0.24± 0.01 – 2.58± 0.15 1.73± 0.10 0.03656 14.9± 0.3 13.9± 3.0 3.61± 0.14 4.07± 1.51 39.85± 1.52 27.26± 1.04 0.03657 11.0± 0.1 10.7± 1.6 2.89± 0.09 3.09± 0.95 15.59± 0.48 7.46± 0.23 0.05158 11.1± 0.1 – 1.16± 0.03 – 15.37± 0.42 11.51± 0.31 0.03259 13.1± 0.5 10.8± 1.7 0.66± 0.06 0.96± 0.30 9.83± 0.84 7.81± 0.67 0.03160 10.3± 0.2 – 4.22± 0.21 – 14.75± 0.72 5.68± 0.28 0.06361 18.4± 0.1 14.9± 3.5 1.19± 0.02 1.67± 0.66 16.04± 0.27 12.15± 0.21 0.03262 10.8± 0.1 – 0.55± 0.03 – 7.30± 0.33 5.46± 0.25 0.03263 11.0± 0.2 – 1.57± 0.07 – 6.72± 0.29 2.86± 0.12 0.057

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Table 5. – continued.

Source THerschel TSCUBA-2 M(THerschel) M(TSCUBA-2) N(H2) n(H2) Deconv.Index (K) (K) (M⊙) (M⊙) (×1021 cm−2) (×104 cm−3) FWHM (pc)

64 10.2± 0.1 – 1.05± 0.04 – 13.82± 0.46 10.31± 0.35 0.03365 11.4± 0.1 – 0.33± 0.02 – 3.45± 0.25 2.30± 0.16 0.03666 11.1± 0.1 – 0.87± 0.03 – 7.58± 0.26 4.62± 0.16 0.04067 11.4± 0.1 – 0.18± 0.01 – 3.18± 0.26 2.76± 0.23 0.02868 11.4± 0.1 – 0.81± 0.03 – 6.63± 0.23 3.91± 0.14 0.04169 13.0± 0.1 – 0.11± 0.01 – 2.64± 0.27 2.70± 0.28 0.02470 12.4± 0.1 – 0.11± 0.01 – 2.03± 0.22 1.76± 0.19 0.02871 10.7± 0.1 11.6± 2.0 2.09± 0.07 1.80± 0.59 11.78± 0.39 5.75± 0.19 0.05072 11.1± 0.1 – 0.32± 0.02 – 3.46± 0.24 2.36± 0.16 0.03673 12.5± 0.0 – 0.09± 0.01 – 1.35± 0.17 1.09± 0.14 0.03074 12.0± 0.0 – 0.19± 0.01 – 2.36± 0.16 1.71± 0.12 0.03475 11.1± 0.0 – 0.23± 0.02 – 3.09± 0.20 2.31± 0.15 0.03276 14.4± 0.1 – 0.09± 0.01 – 2.12± 0.23 2.17± 0.24 0.02477 13.0± 0.0 – 0.10± 0.01 – 1.30± 0.14 0.97± 0.10 0.03278 12.1± 0.1 – 0.28± 0.02 – 2.50± 0.18 1.54± 0.11 0.03979 12.9± 0.0 – 0.09± 0.01 – 1.18± 0.15 0.90± 0.11 0.03280 12.8± 0.0 – 0.18± 0.01 – 2.47± 0.17 1.87± 0.13 0.03281 13.5± 0.0 – 0.08± 0.01 – 1.38± 0.18 1.20± 0.16 0.02882 11.9± 0.1 11.1± 1.8 1.49± 0.05 1.70± 0.54 17.66± 0.56 12.53± 0.39 0.03483 11.7± 0.0 – 0.10± 0.01 – 2.15± 0.28 2.07± 0.27 0.02584 12.2± 0.1 – 0.34± 0.02 – 5.74± 0.26 4.85± 0.22 0.02985 11.8± 0.1 – 0.08± 0.01 – 1.06± 0.18 0.79± 0.13 0.03286 12.0± 0.1 – 0.17± 0.01 – 2.41± 0.20 1.88± 0.16 0.03187 12.6± 0.1 – 0.09± 0.01 – 1.48± 0.20 1.26± 0.17 0.02988 12.3± 0.1 – 0.15± 0.02 – 1.16± 0.13 0.67± 0.08 0.04289 11.9± 0.1 – 0.17± 0.02 – 1.66± 0.18 1.07± 0.12 0.03890 11.8± 0.1 – 0.29± 0.02 – 2.57± 0.15 1.57± 0.09 0.04091 11.9± 0.2 – 0.38± 0.03 – 3.10± 0.22 1.82± 0.13 0.04192 12.5± 0.0 – 0.13± 0.01 – 2.24± 0.21 1.94± 0.18 0.02893 10.8± 0.1 – 1.90± 0.07 – 7.13± 0.27 2.84± 0.11 0.06194 12.1± 0.0 – 0.13± 0.01 – 1.66± 0.16 1.24± 0.12 0.03295 11.4± 0.1 – 1.96± 0.06 – 5.57± 0.17 1.93± 0.06 0.07096 12.4± 0.1 – 0.54± 0.02 – 3.02± 0.11 1.48± 0.05 0.05097 12.3± 0.1 – 0.17± 0.01 – 1.65± 0.14 1.05± 0.09 0.03898 11.7± 0.1 – 0.22± 0.01 – 3.79± 0.16 3.25± 0.14 0.02899 11.8± 0.1 – 0.10± 0.01 – 3.85± 0.25 4.97± 0.32 0.019100 11.6± 0.1 – 0.20± 0.01 – 2.76± 0.14 2.11± 0.11 0.032101 12.4± 0.0 – 0.17± 0.01 – 2.58± 0.12 2.07± 0.10 0.030102 12.2± 0.1 – 0.05± 0.01 – 2.09± 0.25 2.71± 0.32 0.019

103 13.1± 0.1 – 0.05± 0.01 – 1.88± 0.20 2.44± 0.26 0.019104 11.8± 0.1 – 0.07± 0.01 – 2.12± 0.19 2.37± 0.21 0.022105 13.2± 0.0 – 0.01± 0.00 – 0.66± 0.25 1.01± 0.38 0.016106 11.3± 0.2 – 0.86± 0.04 – 5.39± 0.23 2.78± 0.12 0.047107 11.7± 0.1 – 0.12± 0.01 – 2.91± 0.19 2.99± 0.19 0.024108 13.3± 0.1 – 0.04± 0.01 – 0.89± 0.13 0.82± 0.12 0.026109 13.7± 0.1 – 0.02± 0.00 – 1.00± 0.18 1.31± 0.23 0.019110 13.3± 0.1 – 0.03± 0.00 – 1.70± 0.26 2.58± 0.39 0.016111 12.5± 0.1 9.8± 1.4 0.98± 0.02 1.57± 0.46 38.47± 0.64 49.75± 0.83 0.019112 12.5± 0.0 – 0.03± 0.00 – 1.17± 0.21 1.58± 0.29 0.018113 12.3± 0.1 – 0.08± 0.01 – 1.57± 0.13 1.42± 0.12 0.027114 13.0± 0.0 – 0.03± 0.00 – 1.32± 0.21 1.81± 0.28 0.018115 13.0± 0.0 – 0.11± 0.01 – 2.20± 0.11 2.06± 0.11 0.026116 12.5± 0.1 – 0.05± 0.01 – 1.90± 0.22 2.47± 0.28 0.019117 11.8± 0.0 – 0.09± 0.01 – 2.22± 0.17 2.33± 0.17 0.023

of source masses – from their SCUBA-2 850µm flux densi-ties – below. All of our sources were observed as part of theHerschel GBS. However, the sources on the western edgeof L1152 are on the very edge of the Herschel field, andhence their temperatures may be less reliable than those inother parts of the region. Temperatures of cores without em-bedded sources are typically in the range 9–15K, except in

the NGC7023 (L1174) region, where temperatures of up to∼ 50K are measured.

Source masses were determined using the Hildebrand(1983) formulation

M =F totalν (850µm)D2

κν(850µm)Bν(850µm)(T ), (2)

c© 2016 RAS, MNRAS 000, 1–29

14 K. Pattle et al.

where Fν(850µm) is the best-fit model flux density at850 µm, D is the source distance as listed in Table 1,Bν(850µm)(T ) is the Planck function, and κν(850µm) is thedust mass opacity as parameterised by Beckwith et al.(1990), where β is again taken to be 2.0. Note that equation 2is functionally identical to equation 1. However, we deter-mine the masses of our sources using our model SCUBA-2 850-µm flux densities and Herschel -determined temper-atures, whereas equation 1 was used to determine best-fitsource temperatures by fitting the flux densities measuredin four Herschel wavebands to each pixel in the Herschel ob-servations. We use the mean fitted temperature in the pixelsenclosed by the source apertures shown on Figure 6. Detec-tion of a SCUBA-2 source does not necessarily mean thatthere is a Herschel source at the same position.

Mean source volume densities were determined usingthe equation

n(H2) =M

µmh

143πR3

, (3)

where R is the equivalent deconvolved mean FWHM ofthe source. The equivalent deconvolved mean FWHM wastaken to be the geometric mean of the best-fit major andminor FWHMs, with the JCMT 850µm effective beamFWHM (14.1′′) subtracted in quadrature. The mean molec-ular weight µ was taken to be 2.86, assuming that the gasis ∼ 70% H2 by mass (Kirk et al. 2013). We give densi-ties in terms of H2 rather than of total density of particlesas the density ranges traced by different molecular speciesare typically expressed in terms of H2 number density (see,e.g., Di Francesco et al. 2007). The range of densities tracedby isotopologues of CO is relevant to our determination ofcore stability in Section 7, below, and so we express parti-cle number density in terms of n(H2) throughout this work.Assuming a typical mean particle mass of 2.3 amu, our H2

number densities can be converted to total gas particle num-ber densities by multiplication by a factor of 1.24.

Mean source column densities were determined usingthe equation

N(H2) =M

µmh

1

πR2, (4)

with symbols defined as above.The derived properties of our sources: temperature,

mass, column density, volume density, and deconvolvedFWHM, are listed in Table 5. For the protostellar sourcesin our catalogue, the temperatures, and hence the masses,determined from the dust emission are those of the proto-stellar envelopes, and not of the protostars themselves (see,e.g., Pattle et al. 2015). The modified blackbody model usedto fit temperatures is applicable only to envelope-dominatedsources; the temperatures and masses determined for theClass II and III protostars in our catalogue (11 sources, listedin Table 4) may not be representative.

3.4 SCUBA-2-derived temperatures and masses

We derived temperatures for our sources from the ratio ofthe total SCUBA-2 450-µm and 850-µm flux densities mea-sured along the line of sight for each source. The tempera-ture of a source can be determined from measurements of

Figure 7. Comparison of SCUBA-2- and Herschel-derived (DiFrancesco et al., 2016, in prep.) temperatures. Red sources lie inL1147/58, light green sources in L1174, blue sources in L1251,and purple sources in L1228. Error bars show 1-σ uncertaintiesas listed in Table 5. The dashed line is the 1:1 line.

Figure 8. Comparison of source masses determined usingSCUBA-2- and Herschel-derived (Di Francesco et al., 2016, inprep.) temperatures. Red sources lie in L1147/58, light greensources in L1174, blue sources in L1251, and purple sources inL1228. Error bars show 1-σ uncertainties as listed in Table 5.The dashed line is the 1:1 line.

flux densities Fν1 and Fν2 at frequencies respectively ν1 andν2 using the relation

Fν1

Fν2

=

(

ν1ν2

)3+βe

hν2

kbT − 1

ehν1

kbT − 1, (5)

where T is the source temperature and β is the dust opacityindex, as before (see, e.g., Buckle et al. 2015). Assuming

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First SCUBA-2 observations of Cepheus 15

Figure 9. Comparison of source mass (determined using Herschel-derived temperatures) and source size (geometric mean of modelledmajor and minor FWHMs) for the sources in Cepheus. Circles represent starless cores; stars represent cores with embedded protostars.Red sources lie in L1147/58, light green sources in L1174, dark green sources in L1172, blue sources in L1251, and purple sources inL1228.

β = 2.0, then in the case of the ratio of SCUBA-2 450-µmand 850-µm fluxes this relation becomes

Fν(450µm)

Fν(850µm)= 24.05 × e16.96/T − 1

e32.02/T − 1. (6)

This equation can be solved numerically for source tempera-ture T . This analysis presumes that the 450-µm and 850-µmemission traces the same dust population, and that the line-of-sight temperature variation is minimal (see, e.g., Shettyet al. 2009). A detailed analysis of dust temperatures deter-mined from SCUBA-2 450-µm and 850-µm observations ofthe W40 region was performed by Rumble et al. (2016). Wechoose β = 2.0 for consistency with the Herschel -derivedtemperature measurements, as described above.

As discussed in Section 3.2, 450-µm aperture photom-etry measurements were made using data which were con-volved to match the resolution of the 850-µm data using aconvolution kernel constructed as described by Pattle et al.(2015), using the SCUBA-2 450-µm and 850-µm beam mod-els given by Dempsey et al. (2013).

We derived temperatures for those of our sources witha detection > 5σ at SCUBA-2 450µm. These tempera-tures are listed in Table 5. Figure 7 compares the temper-atures derived using SCUBA-2 and Herschel data, showingthat SCUBA-2-derived and Herschel -derived source temper-atures (Di Francesco et al., 2016, in prep.) are typically in

agreement, albeit with large uncertainties on the SCUBA-2-derived temperatures.

This analysis suggests that determining source temper-atures using only the ratio of SCUBA-2 450-µm and 850-µmdata will produce reliable results in low-temperature cores.This is as expected, as equation 5 is insensitive to temper-ature in the Rayleigh-Jeans (RJ) limit (hν/kbT ≪ 1). The450-µm data point will fall on the RJ tail of the spectralenergy distribution if T ≫ 32K, while the 850-µm datapoint will fall on the RJ tail if T ≫ 17K. It can be seenin Figure 7 that the uncertainties on our SCUBA-2-derivedtemperatures increase substantially when T > 20K, due tothe decreasing sensitivity of the flux density ratio to tem-perature as source temperature increases.

Figure 7 shows that there is a slight tendency for sourcetemperatures determined from Herschel measurements tobe higher than those determined from SCUBA-2 measure-ments. While this behaviour is not statistically significant,this is consistent with the shorter-wavelength Herschel ob-servations being sensitive to emission from warmer materialthan the longer-wavelength SCUBA-2 observations.

We calculated the masses of each of our sources us-ing equation 2, our SCUBA-2-derived temperatures, and ourbest-fit model 850-µm flux densities. Source masses deter-mined from SCUBA-2 temperatures are listed in Table 5.Figure 8 compares the masses derived using SCUBA-2-basedand Herschel -based source temperatures (Di Francesco et

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16 K. Pattle et al.

Figure 10. Comparison of temperature and density for the sources in Cepheus. Colour and symbol coding is as in Figure 9 (red –L1147/58; light green – L1172; dark green – L1174; blue – L1251; purple – L1228).

al., 2016, in prep.), and shows that the two measures ofmass are generally in agreement. There is a slight tendencyto SCUBA-2-temperature masses to be higher than Her-

schel -temperature masses. This is a result of the tendencyfor Herschel -derived temperatures to be higher than thosederived from SCUBA-2 data.

Thus, we conclude that there is reasonable agreementbetween SCUBA-2-derived and Herschel -derived sourcetemperatures for our sources, and that SCUBA-2-derivedsource temperatures will be accurate when there is a good(> 5σ) source detection at 450-µm, and when neither the450-µm nor the 850-µm data point falls on the Rayleigh-Jeans tail of the spectral energy distribution. For a detailedcomparison of core properties determined from SCUBA-2and Herschel data, see Ward-Thompson et al. (2016).

4 DISCUSSION OF DERIVED PROPERTIES

The masses and sizes of our sources are shown in Figure 9.Our sources typically occupy the upper part of the mass/sizeplane, in which prestellar cores are expected to lie (Simp-son, Nutter & Ward-Thompson 2008), being overdense rela-tive to transient, unbound structure (c.f. Andre et al. 2010).The grey band on Figure 9 shows the region in which tran-sient, gravitationally-unbound CO clumps are expected tolie (Elmegreen & Falgarone 1996).

The temperatures and volume densities of our sourcesare shown in Figure 10. It can be seen that with the ex-ception of sources in L1174 – the reflection nebula – the

cores in our sample have a narrow range of temperatures(∼ 9− 15K).

In order to determine a mass function for each set ofstarless cores in our sample, we analysed the cumulativedistribution functions of starless core masses for each regionin Cepheus, using the maximum likelihood estimator for aninfinite power-law distribution (Koen 2006; Maschberger &Kroupa 2009). Throughout the following discussion we as-sume that the masses of cores can be modelled by a power-law function,

ξ(M)dM ∝ M−αdM, (7)

where ξ(M)dM is the number of cores in the mass range Mto M + dM .

The empirical cumulative distribution function F isgiven, for the ith data point in our sample, by

F (Xi) ≡i

n+ 1, (8)

where n is the number of data points X. The maximumlikelihood (ML) estimator for the exponent α of an infinitepower-law distribution is

αml = 1 +n

(∑n

i=1 ln (Xi))

− nln (min(X)). (9)

The unbiased maximum likelihood (UML) estimator, αuml

is then

αuml = 1 +n− 1

n(αml − 1). (10)

Uncertainties were estimated by performing a set of MonteCarlo experiments, drawing a set of data points randomly

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First SCUBA-2 observations of Cepheus 17

Figure 11. Cumulative probability plots by region. Colour coding is as in Figure 9 (red – L1147/58; light green – L1172; blue – L1251;purple – L1228).

from our distribution of masses, from which αml was recal-culated. The error quoted is the standard deviation of thedistribution of αuml which results from this procedure.

In this analysis we consider only starless cores, exclud-ing all sources with embedded objects. This is in order toconstruct cumulative mass distributions comparable to thecore mass function (CMF).

The cumulative mass distribution functions for each re-gion of Cepheus except L1172 are shown in Figure 11, whilethe cumulative mass distribution function for all of the star-less cores in our sample combined is shown in Figure 12.The maximum-likelihood-estimator mass functions for eachregion are listed in Table 6. L1172 is excluded from thisanalysis as the region contains only 7 starless cores, too few

to accurately constrain the power-law index of the region’score mass function.

As can be seen from Figure 11 and Table 6, the coremass function in each region in the Cepheus Flare other thanL1172 can be characterised by a power law above a mass of0.05M⊙. The L1147/58, L1174 and L1251 αuml values aresimilar, and show a high-mass CMF slope of αuml = 1.8 ±0.2, 2.0 ± 0.2 and 1.8 ± 0.1 respectively. The L1228 region,however, has a high-mass CMF slope of αuml,L1228 = 2.3 ±0.3. Whether this difference in CMF slope is indicative ofa difference in behaviour between L1228 and the remainderof the sample, or merely of the small sample sizes in eachregion, is difficult to determine.

We combined the cores from each individual region in

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Figure 12. Cumulative probability plots for the starless cores in Cepheus. Left panel: power-law distribution for cores with masses> 0.08M⊙. Right panel: power-law distribution for cores with masses > 0.5M⊙. Colour coding is as in Figure 9 (red – L1147/58; lightgreen – L1172; dark green – L1174; blue – L1251; purple – L1228).

order to overcome the problem of small number statistics.The cumulative mass distribution for all of the starless coreswe detect in Cepheus (including those in L1172) is shownin Figure 12. There appears to be a break in starless coremasses between 0.3 and 0.5 M⊙, with no starless cores beingdetected in this mass range. Determining αuml over the massrange M > 0.08M⊙ gives a power-law index of 1.9 ± 0.1,with starless cores in the mass range 0.08 − 0.3M⊙ con-forming well to a power-law distribution (see left panel ofFigure 12). Determining αuml for the high-mass cores only(M > 0.5M⊙) gives a steeper power-law index, of 2.6± 0.3.Whether these high-mass starless cores represent a differentpopulation is not clear.

Both Chabrier (2003) and Kroupa (2001) predict apower-law index of 2.3 for the high-mass end of the stellarInitial Mass Function (IMF), consistent with the Salpeter(1955) high-mass IMF. Previously, a number of authors havesuggested a link between the stellar IMF and the CMF(e.g. Motte, Andre & Neri 1998; Nutter & Ward-Thompson2007). In Cepheus we see a high-mass CMF slope of 2.6±0.3(when M > 0.5M⊙), consistent with the Kroupa-Chabrier-Salpeter value.

The break in core masses can be seen in Figure 9, forboth starless cores (as discussed in this section) and for coreswith embedded protostars. Inspection of Figure 9 furthershows that these most massive cores have a higher averageradius than the rest of the population. This might suggestthat the more massive cores without embedded sources are aseparate population of starless ‘clumps’; objects which mightbe expected to fragment to form multiple starless cores.The lower-mass population of starless clumps might, due totheir large radii and low masses and temperatures, be belowthe detectability limit of SCUBA-2 (Ward-Thompson et al.2016). However, whether these highest-mass objects are infact a separate population is by no means certain.

Table 6. Maximum-likelihood-estimator power law indices forcores in Cepheus

Region αuml Mass Range

L1147/L1158 1.8± 0.2 > 0.05M⊙

L1174 2.0± 0.2 > 0.05M⊙

L1251 1.8± 0.1 > 0.05M⊙

L1228 2.3± 0.3 > 0.05M⊙

All 1.9± 0.1 > 0.08M⊙

All 2.6± 0.3 > 0.5M⊙

5 COUNTING STATISTICS

We compared the number of starless cores in our samplewith the number of embedded (Class I and Flat) and ClassII sources detected by K09 in the same area, in order tomake a crude estimate of the relative level of star formationactivity in the different regions of the Cepheus Flare. Theabsolute number counts are shown in Figure 13, while thecounts normalised to the number of Class II sources in theregion are shown in Figure 14.

Figure 13 shows that in absolute terms, L1251 containsthe highest number of both starless cores and embeddedsources, and the second highest number of Class II sources.L1174 contains the highest number of Class II sources; anatural result for a region in which clustered star forma-tion has been ongoing for some time (Kun, Kiss & Balog2008). L1174 has the second highest number of embeddedsources after L1251, and the joint second-highest number ofstarless cores, along with L1228. L1228, L1147/L1158 andL1172 have low number counts of both embedded and ClassII sources. This shows that the sites of ongoing active starformation, L1251 and L1174, have the highest absolute num-ber of sources in almost all categories, while the regions ofless active star formation generally have lower numbers ofstarless cores as well as of embedded sources. However, inorder to determine the evolutionary status of each region,the ratio of starless cores to embedded sources must be con-sidered.

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First SCUBA-2 observations of Cepheus 19

Figure 13. Regional statistics of absolute number of starless,embedded and Class II sources in Cepheus. Colour coding is asin Figure 9 (red – L1147/58; light green – L1172; dark green –L1174; blue – L1251; purple – L1228).

Figure 14. Regional statistics of starless, embedded and Class IIsources in Cepheus, normalised to the number of Class II sources.Colour coding is as in Figure 9 (red – L1147/58; light green –

L1172; dark green – L1174; blue – L1251; purple – L1228).

Figure 14 shows the number of sources of each type ineach region, normalised to the number of Class II sources.Again, a difference in behaviour can be seen between theless active regions, L1147/58 and L1228, and the active re-gions L1174 and L1251. In the less active regions, there is ahigh ratio of starless cores to Class II sources: ∼ 3.8 : 1 inL1148/L1157, and ∼ 2.7 : 1 in L1228. However, in the activestar-forming regions, this ratio is much lower: ∼ 1.4 : 1 inL1251, while in L1174 Class II sources outnumber starlesscores, with a ratio ∼ 0.7 : 1. L1172 shows an intermediatebehaviour, with a ratio ∼ 1.8 : 1. However, the low countingstatistics in all classes in L1172 make any interpretation ofthis result difficult.

Since we do not know whether the star formation rate(SFR) in Cepheus has been constant over time, we consider

two scenarios: a constant SFR over a very long time or arelatively short and finite burst of star formation.

In the first scenario, we can interpret those regions witha lower ratio of starless cores to Class II sources (L1251 andL1174) as having a high (but constant) SFR, i.e. convertinggas into stars efficiently. Those regions with a higher ratioof starless cores to Class II sources (L1147/58 and L1228),we interpret as having a lower (but still constant) SFR, i.e.these regions are forming stars less efficiently.

In the second scenario, we can interpret those regionswith a higher ratio of starless cores to Class II sources as be-ing at an earlier evolutionary stage than those with a lowerstarless core to Class II ratio, i.e. the regions with a highratio have thus far converted only a small amount of theirreservoir of available material into stars, while the regionswith a low ratio have significantly depleted their local reser-voir of dense gas.

The ratios which we observe are likely to result from acombination of these effects. We can attempt to determinewhich effect is more likely to dominate for each region byconsidering what we know of their star formation historiesand the current or historical influences on them. However,all of the following intepretation must be used with care,as our absolute number counts of cores and Class II sourcesmay not be large enough to put our conclusions on a stronglystatistically-significant footing.

Star formation in L1251 may have been triggered or en-hanced by passage of the Cepheus Flare Shell (CFS) throughthe region ∼ 4Myr ago, while L1228 may currently be in-teracting with the CFS (see Section 3.1, above). This is con-sistent with the high starless-core-to-Class-II ratio in theseregions resulting from the second scenario described above,with the low core-to-Class-II ratio in L1251 indicating thatthe region is significantly more evolved than L1228, in whichstar formation has only recently been triggered or enhanced.

L1147/58, with a high core-to-Class-II ratio, shows nosignificant signs of recent external influence (see Section 3.1,above), suggesting that here the first scenario might be morelikely, and star formation is an ongoing, inefficient process.The clustered star formation in L1174 (low core-to-Class-II ratio) is more difficult to interpret; star formation hasbeen ongoing in this region for some time, suggesting thatL1174 might be running out of gas to convert into stars, thusfavouring the first scenario.

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Figure 15. BE stability plot for starless cores in Cepheus, with observed mass plotted against the Bonnor-Ebert critically-stable mass.Left panel: bounding density ne = 103 cm−3; right panel: bounding density ne = 104 cm−3. Cores to the right of the dashed line haveno stable Bonnor-Ebert configuration. Colour coding is as in Figure 9 (red – L1147/58; light green – L1172; dark green – L1174; blue –L1251; purple – L1228).

6 BONNOR-EBERT STABILITY ANALYSIS

The Bonnor-Ebert (BE) model of a starless core (Ebert1955; Bonnor 1956) is frequently used as a measure ofthe stability of starless cores (e.g. Alves, Lada & Lada2001). The BE model treats a core as an isothermal, self-gravitating, polytropic sphere bounded by external pres-sure. For a given core temperature and external pressure,there is a maximum mass at which the core can be stableagainst gravitational collapse. The critically-stable Bonnor-Ebert mass is frequently used as a proxy for virial mass(e.g. Konyves et al. 2015). In the following analysis, we con-sider the stability of the starless cores in Cepheus againstgravitational collapse according to the Bonnor-Ebert model,under the assumption that our cores can be accurately char-acterised as Bonnor-Ebert spheres. As discussed above, de-tailed modelling of core geometries is beyond the scope ofthis study, and so we cannot definitively state whether ourcores have morphologies consistent with the Bonnor-Ebertmodel.

6.1 Choice of bounding radius

As discussed above, the BE model treats cores as beingbound by external pressure. We have hitherto modelled ourcores as having Gaussian density distributions, without adefined edge radius.

We define our edge radius re as

re = α

√

2 ln

(

ρ0ρe

)

, (11)

where ρ0 is the central density of the core and ρe is thedensity at the pressure-confined edge, assuming that the coreobeys a Gaussian density distribution at all radii smallerthan the edge radius.

The central density ρ0 can be determined from the mod-elled mass M and Gaussian width α of each core (listed inTable 5):

ρ0 =M

(2πα2)3

2

. (12)

We here consider two different bounding densities,

ρe = µmh × 104 cm−3, (13)

and

ρe = µmh × 103 cm−3, (14)

as representing a physically plausible range of densities atwhich our cores might be bound, and for consistency withour analysis of external pressure based on measurements of13CO linewidths in Section 7, below. These choices of bound-ing density are consistent with our measurements: Figure 10shows that the mean density of our cores is & 104 cm−3 inalmost all cases (the exceptions being warm, low-column-density cores in L1174), and in all of our cores, the centraldensity inferred using equation 12 is > 104 cm−3 (see Ta-ble 7).

6.2 Critically-stable Bonnor-Ebert sphere

The mass at which a BE sphere at temperature T , withsound speed cs(T ), and bounded by external pressure Pext,is critically stable against gravitational collapse is given by

Mbe,crit = 1.18cs(T )

4

P1/2ext G3/2

. (15)

This can alternatively be expressed in terms of the critically-stable Bonnor-Ebert radius Rbe,crit,

Mbe,crit = 2.4c2sGRbe,crit = 2.4

kbT

µmhGRbe,crit. (16)

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In an attempt to determine whether our starless coresare likely to be virially bound, we determined their Bonnor-Ebert critically-stable masses (Ebert 1955; Bonnor 1956),under the assumption that Rbe,crit = re . The critically-stable Bonnor-Ebert masses of our cores are listed in Table 7,and are plotted against our observed core masses in Fig-ure 15. Figure 15 suggests that the majority of our cores havestable, pressure-confined (i.e. non-critical) Bonnor-Ebert so-lutions. Our choice of bounding density does not signifi-cantly affect which of our cores have stable Bonnor-Ebertsolutions.

7 ENERGY BALANCE AND STABILITY

We attempted to assess the energy balance of the starlesscores in the Cepheus molecular cloud and to determine theapplicability of our Bonnor-Ebert analysis by estimating theexternal pressure on our cores using measurements presentedby Yonekura et al. (1997) (hereafter Y97). Y97 conducteda large-scale 13CO J = 1 → 0 survey of the Cepheus Flareregion using two 4-m telescopes at Nagoya University. Theirobservations had a resolution of 2.4 arcmin. Each of theregions in our survey is entirely covered by a different, single,Y97 source: Y97 Source 8 for L1147/58, Y97 Source 14 forL1172 and L1174, Y97 Source 79 for L1251, and Y97 Source66 for L1228. Thus, we can estimate only a single value forexternal pressure in each region, which we then assume isrepresentative for all of the cores within that region.

Previous studies of starless cores suggested that exter-nal gas pressure might be instrumental in confining densecores in at least some cases (Maruta et al. 2010; Pattle et al.2015). We apply the method used by Pattle et al. (2015)to estimate the external pressure on starless cores in theOphiuchus molecular cloud to our sample of starless cores.

We consider the gas pressure in material traced by 13COto be the external pressure acting on our starless cores, sinceCO is expected to trace the outer layers, or envelopes, ofstarless cores (Di Francesco et al. 2007). Higher-density trac-ers such as N2H

+ are expected to trace the denser innermaterial of the cores themselves.

We estimate the external pressure Pext in each regionfrom the linewidths measured by Y97 using the ideal gaslaw

Pext ≈ ρ13co〈σ2

gas,13co〉. (17)

We consider two different models of the gas pressure in ma-terial traced by 13CO. In the first instance, we assume thatour cores are bounded at the maximum gas density tracedby 13CO, ρ13

co∼ 104 cm−3 (Di Francesco et al. 2007). We

also consider the case in which our cores are bounded at the‘typical’ density of gas traced by 13CO, ρ13

co∼ 103 cm−3 (Di

Francesco et al. 2007). Hereafter, we refer to these models as‘high-bounding-density’ and ‘low-bounding-density’ respec-tively.

The measured mean density of material within a molec-ular cloud depends strongly on the volume over which itis being assessed. Using the values of total mass and sur-face area for Cepheus listed by Dunham et al. (2015),2610 ± 170M⊙ and 38 pc2 respectively, we find, assuminga spherical geometry, 〈n(H2)〉 = 210 cm−3. This value isdetermined over all areas mapped by Spitzer with AV & 3.

However, K09 list a total cloud mass of 1003M⊙ over a totalarea of 0.4 pc2, considering only areas with AV > 5. Againassuming a spherical geometry, this implies a mean volumedensity 〈n(H2)〉 = 7.5 × 104 cm−3. Moreover, the sizes andmasses listed for individual clumps by K09 suggest densities∼ 105 cm−3 in at least some star-forming clumps. Where inthis range of densities our ‘bounding density’ – i.e. the min-

imum density of material associated with a potentially star-

forming core – is likely to fall is not immediately clear. How-ever, the apparent threshold for star formation of AV ∼ 7(or higher) in local clouds (e.g. Molinari et al. 2014, and ref-erences therein) suggests that star-forming cores are likely toexist within regions with densities significantly higher thanthe mean value in the cloud.

As discussed above, we typically find mean core densi-ties ∼ 104 cm−3 in our sample, and infer peak core densities> 104 cm−3 but generally < 105 cm−3 (with some exceptionsin the densest cores). Hence, we assume that the boundingdensities of our cores cannot significantly exceed 104 cm−3,and are likely to be lower. Assuming that potentially star-forming cores exist within regions of density higher than thebackground cloud average, we consider 103−104 cm−3 to berepresentative of the range of densities at which our coresare likely to be bound.

Y97 find the highest 13CO linewidth in L1251, the low-est in L1147/L1158, and the same, intermediate, value inL1172, L1174 and L1228. It is possible that there are, lo-cally, higher external pressures within these regions thanare captured by the low-resolution Y97 measurements.

In the following analysis, we treat both the thermal andnon-thermal components of the velocity dispersion in 13COas representing a hydrostatic pressure on our cores – i.e.we are treating the non-thermal component of the velocitydispersion as a modification to the sound speed in the gas(the microturbulent assumption; Chandrasekhar 1951a,b).Whilst on the majority of size scales in molecular cloudsthis has been demonstrated to be an invalid assumption, ithas been shown that in both the compressible and incom-pressible cases, turbulence can provide support against cloudcollapse (and hence, conversely, can provide an ‘inward’ pres-sure promoting collapse) on scales smaller than the thermalJeans wavelength in the cloud (Mac Low & Klessen 2004,and references therein). For typical conditions in our cores,T ∼ 15K and n(H2) ∼ 104 cm−3, the thermal Jeans wave-length (λJ = cs

√

π/(Gρ), where cs is sound speed and ρ isgas density; Jeans 1928) in our cores is λJ ∼ 0.2 pc, an orderof magnitude larger than the size scale of our cores (see Ta-bles 5 and 7). Hence, the assumption that the non-thermalcomponent of the velocity dispersion can be treated as ahydrostatic pressure is justifiable in the case of our cores.

7.1 Virial analysis of cores in Cepheus

We performed a virial analysis on our cores, in order to testtheir stability against collapse, and hence to test the validityof the Bonnor-Ebert analysis above. We estimate the termsin the virial equation, in order to determine the stabilityof our cores. Throughout the following analysis, we assumethat our cores obey a Gaussian core density profile, consis-tent with the core fitting process discussed in Section 3.2.

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22 K. Pattle et al.

Table 7. Data relating to starless cores’ virial stability: (1) core ID, (2) modelled peak density, (3) gas velocity dispersion determinedfrom low-resolution Y97 13CO measurements, (4,5,6,7) modelled bounding radius, external pressure, Bonnor-Ebert critically-stable mass,and ratio of observed to BE-critical mass, for a bounding density of n(H2)= 103 cm−3, (8,9,10,11) as 4–7, for a bounding density ofn(H2)= 104 cm−3.

n(H2)= 103 cm−3 n(H2) = 104 cm−3

Source n0 σ13co,gas

r13co

FWHM

Pext/kb Mbe M

Mbe

r13co

FWHM

Pext/kb Mbe M

MbeID (×104 cm−3) (kms−1) (Kcm−3) (M⊙) (Kcm−3) (M⊙)

3 35.45± 1.58 0.4 1.46 0.6 0.969± 0.017 1.35± 0.08 1.13 6.2 0.768± 0.013 1.71± 0.104 22.23± 0.63 0.4 1.40 0.6 1.307± 0.018 1.30± 0.08 1.06 6.2 0.957± 0.013 1.77± 0.107 5.82± 0.98 0.4 1.21 0.6 0.847± 0.003 0.31± 0.02 0.80 6.2 0.596± 0.002 0.44± 0.038 5.87± 0.70 0.4 1.21 0.6 0.998± 0.008 0.32± 0.03 0.80 6.2 0.659± 0.005 0.49± 0.049 61.65± 1.77 0.4 1.52 0.6 0.759± 0.008 0.22± 0.03 1.22 6.2 0.525± 0.006 0.32± 0.0410 7.03± 0.45 0.4 1.24 0.6 0.838± 0.006 0.31± 0.02 0.84 6.2 0.590± 0.004 0.44± 0.0312 6.10± 0.65 0.4 1.22 0.6 0.750± 0.005 0.15± 0.02 0.81 6.2 0.471± 0.003 0.25± 0.0413 7.02± 0.50 0.4 1.24 0.6 0.760± 0.003 0.20± 0.02 0.84 6.2 0.511± 0.002 0.30± 0.0314 10.52± 0.98 0.4 1.30 0.6 0.706± 0.003 0.18± 0.02 0.92 6.2 0.481± 0.002 0.27± 0.0315 3.32± 0.48 0.4 1.12 0.6 0.743± 0.002 0.15± 0.02 0.66 6.2 0.494± 0.001 0.22± 0.0316 4.47± 0.60 0.4 1.17 0.6 0.740± 0.003 0.08± 0.02 0.73 6.2 0.441± 0.002 0.14± 0.0317 4.94± 0.52 0.4 1.19 0.6 0.601± 0.003 0.14± 0.03 0.76 6.2 0.413± 0.002 0.21± 0.0418 3.69± 0.52 0.4 1.14 0.6 1.368± 0.006 0.47± 0.03 0.69 6.2 0.814± 0.004 0.80± 0.0419 5.42± 0.67 0.4 1.20 0.6 0.681± 0.002 0.06± 0.02 0.78 6.2 0.340± 0.001 0.11± 0.0320 4.57± 0.57 0.4 1.17 0.6 1.442± 0.013 0.63± 0.04 0.74 6.2 0.934± 0.008 0.98± 0.0521 4.66± 0.53 0.7 1.18 1.6 1.168± 0.038 0.70± 0.07 0.74 16.0 0.930± 0.030 0.88± 0.0826 3.30± 0.45 0.7 1.12 1.6 0.914± 0.020 1.33± 0.10 0.66 16.0 0.733± 0.016 1.66± 0.1227 3.88± 0.18 0.7 1.15 1.6 2.087± 0.141 0.33± 0.08 0.70 16.0 1.446± 0.098 0.47± 0.1028 4.18± 0.68 0.7 1.16 1.6 1.154± 0.030 0.07± 0.01 0.72 16.0 0.767± 0.020 0.10± 0.0129 6.02± 0.35 0.7 1.22 1.6 1.515± 0.059 0.05± 0.01 0.80 16.0 0.961± 0.038 0.08± 0.01

30 40.02± 2.51 0.7 1.47 1.6 0.927± 0.009 0.10± 0.01 1.15 16.0 0.594± 0.006 0.16± 0.0231 36.13± 1.19 0.7 1.46 1.6 1.024± 0.016 0.15± 0.02 1.14 16.0 0.677± 0.011 0.23± 0.0333 28.02± 2.62 0.7 1.43 1.6 1.175± 0.012 0.03± 0.00 1.10 16.0 0.619± 0.006 0.05± 0.0134 46.19± 1.11 0.7 1.49 1.6 1.425± 0.032 0.13± 0.01 1.18 16.0 0.930± 0.021 0.20± 0.0236 6.17± 0.71 0.7 1.22 1.6 1.012± 0.022 0.11± 0.01 0.81 16.0 0.705± 0.015 0.16± 0.0237 4.54± 0.53 0.7 1.17 1.6 0.872± 0.001 0.09± 0.01 0.74 16.0 0.547± 0.001 0.14± 0.0238 3.48± 0.39 0.7 1.13 1.6 1.623± 0.059 0.14± 0.02 0.67 16.0 1.012± 0.037 0.23± 0.0339 3.68± 0.46 0.7 1.14 1.6 1.897± 0.044 0.08± 0.01 0.69 16.0 1.048± 0.024 0.15± 0.0240 4.42± 0.44 0.7 1.17 1.6 2.489± 0.175 0.25± 0.08 0.73 16.0 1.199± 0.084 0.51± 0.1142 1.78± 0.32 0.7 1.02 1.6 0.708± 0.004 0.12± 0.02 0.46 16.0 0.478± 0.003 0.17± 0.0343 4.06± 0.34 0.7 1.16 1.6 1.073± 0.013 0.05± 0.01 0.71 16.0 0.669± 0.008 0.08± 0.0144 1.07± 0.31 0.7 0.92 1.6 1.381± 0.035 0.11± 0.01 0.15 16.0 0.834± 0.021 0.18± 0.0245 6.49± 0.68 0.7 1.23 1.6 1.304± 0.029 0.05± 0.01 0.82 16.0 0.763± 0.017 0.08± 0.0146 3.27± 0.46 0.7 1.12 1.6 1.015± 0.016 0.12± 0.01 0.65 16.0 0.673± 0.010 0.18± 0.0249 1.48± 0.20 0.7 0.99 1.6 0.661± 0.004 0.16± 0.02 0.38 16.0 0.455± 0.003 0.23± 0.0350 3.15± 0.37 0.7 1.12 1.6 0.680± 0.001 0.11± 0.01 0.64 16.0 0.451± 0.001 0.16± 0.0251 5.04± 0.86 0.7 1.19 1.6 0.701± 0.004 0.11± 0.02 0.76 16.0 0.450± 0.002 0.17± 0.0252 3.19± 0.44 0.7 1.12 1.6 0.722± 0.003 0.14± 0.02 0.65 16.0 0.481± 0.002 0.21± 0.0253 2.76± 0.28 0.7 1.09 1.6 0.727± 0.005 0.11± 0.02 0.61 16.0 0.457± 0.003 0.18± 0.0254 2.44± 0.30 0.7 1.07 1.6 0.647± 0.005 0.11± 0.02 0.57 16.0 0.424± 0.003 0.16± 0.0355 4.49± 0.46 0.7 1.17 1.6 0.916± 0.005 0.27± 0.02 0.74 16.0 0.633± 0.004 0.38± 0.0258 39.98± 1.08 0.8 1.47 2.3 0.875± 0.007 1.33± 0.04 1.15 22.5 0.697± 0.005 1.67± 0.0559 27.11± 2.31 0.8 1.42 2.3 0.947± 0.037 0.70± 0.09 1.09 22.5 0.740± 0.029 0.89± 0.1060 19.73± 0.97 0.8 1.38 2.3 1.488± 0.031 2.84± 0.23 1.04 22.5 1.141± 0.024 3.70± 0.2762 18.98± 0.87 0.8 1.38 2.3 0.799± 0.008 0.69± 0.04 1.03 22.5 0.611± 0.006 0.90± 0.0563 9.94± 0.43 0.8 1.29 2.3 1.349± 0.020 1.16± 0.07 0.91 22.5 0.983± 0.015 1.60± 0.0964 35.80± 1.20 0.8 1.46 2.3 0.802± 0.007 1.32± 0.05 1.14 22.5 0.636± 0.005 1.66± 0.0665 8.00± 0.57 0.8 1.26 2.3 0.872± 0.011 0.38± 0.03 0.87 22.5 0.622± 0.008 0.53± 0.0466 16.04± 0.55 0.8 1.35 2.3 0.993± 0.007 0.87± 0.04 1.00 22.5 0.751± 0.006 1.15± 0.0567 9.58± 0.79 0.8 1.28 2.3 0.685± 0.004 0.26± 0.02 0.90 22.5 0.497± 0.003 0.36± 0.0368 13.57± 0.48 0.8 1.33 2.3 1.044± 0.008 0.78± 0.03 0.97 22.5 0.780± 0.006 1.04± 0.0470 6.12± 0.67 0.8 1.22 2.3 0.707± 0.005 0.16± 0.02 0.81 22.5 0.489± 0.003 0.23± 0.0371 19.98± 0.67 0.8 1.38 2.3 1.225± 0.015 1.71± 0.08 1.04 22.5 0.940± 0.011 2.23± 0.1072 8.18± 0.56 0.8 1.26 2.3 0.835± 0.010 0.38± 0.03 0.87 22.5 0.597± 0.007 0.53± 0.0473 3.78± 0.48 0.8 1.14 2.3 0.723± 0.001 0.12± 0.02 0.69 22.5 0.466± 0.001 0.19± 0.0274 5.94± 0.40 0.8 1.21 2.3 0.820± 0.002 0.23± 0.02 0.80 22.5 0.566± 0.001 0.34± 0.0275 8.03± 0.53 0.8 1.26 2.3 0.756± 0.003 0.31± 0.02 0.87 22.5 0.540± 0.002 0.43± 0.0377 3.38± 0.36 0.8 1.13 2.3 0.800± 0.002 0.12± 0.01 0.66 22.5 0.505± 0.001 0.20± 0.0278 5.36± 0.38 0.8 1.20 2.3 0.955± 0.011 0.29± 0.02 0.78 22.5 0.650± 0.008 0.43± 0.03

c© 2016 RAS, MNRAS 000, 1–29

First SCUBA-2 observations of Cepheus 23

Table 7. – continued.

n(H2)= 103 cm−3 n(H2)= 104 cm−3

Source n0 σ13co,gas

r13co

FWHM

Pext/kb Mbe M

Mbe

r13co

FWHM

Pext/kb Mbe M

MbeID (×104 cm−3) (kms−1) (Kcm−3) (M⊙) (Kcm−3) (M⊙)

79 3.12± 0.40 0.8 1.11 2.3 0.769± 0.002 0.11± 0.01 0.64 22.5 0.478± 0.002 0.18± 0.0280 6.48± 0.45 0.8 1.23 2.3 0.846± 0.003 0.22± 0.02 0.82 22.5 0.590± 0.002 0.31± 0.0281 4.17± 0.54 0.8 1.16 2.3 0.734± 0.003 0.11± 0.01 0.72 22.5 0.481± 0.002 0.16± 0.0283 7.20± 0.95 0.8 1.24 2.3 0.611± 0.002 0.16± 0.02 0.84 22.5 0.431± 0.001 0.23± 0.0385 2.75± 0.46 0.8 1.09 2.3 0.705± 0.005 0.11± 0.02 0.60 22.5 0.425± 0.003 0.19± 0.0386 6.54± 0.55 0.8 1.23 2.3 0.768± 0.006 0.22± 0.02 0.82 22.5 0.536± 0.004 0.31± 0.0387 4.37± 0.60 0.8 1.17 2.3 0.701± 0.004 0.12± 0.02 0.73 22.5 0.463± 0.003 0.19± 0.0388 2.34± 0.26 0.8 1.07 2.3 0.926± 0.004 0.16± 0.02 0.55 22.5 0.536± 0.003 0.27± 0.0389 3.70± 0.40 0.8 1.14 2.3 0.864± 0.010 0.20± 0.02 0.69 22.5 0.555± 0.007 0.31± 0.0490 5.45± 0.32 0.8 1.20 2.3 0.939± 0.004 0.31± 0.02 0.78 22.5 0.640± 0.003 0.46± 0.0392 6.75± 0.64 0.8 1.23 2.3 0.720± 0.003 0.18± 0.02 0.83 22.5 0.504± 0.002 0.25± 0.0293 9.87± 0.38 0.8 1.29 2.3 1.412± 0.018 1.35± 0.08 0.91 22.5 1.028± 0.013 1.85± 0.1094 4.32± 0.42 0.8 1.17 2.3 0.770± 0.002 0.16± 0.02 0.73 22.5 0.508± 0.001 0.25± 0.0295 6.72± 0.21 0.8 1.23 2.3 1.638± 0.015 1.19± 0.05 0.83 22.5 1.146± 0.011 1.71± 0.0796 5.13± 0.19 0.8 1.19 2.3 1.232± 0.005 0.44± 0.02 0.77 22.5 0.833± 0.004 0.65± 0.0397 3.64± 0.31 0.8 1.14 2.3 0.899± 0.004 0.19± 0.02 0.68 22.5 0.575± 0.003 0.30± 0.0398 11.28± 0.48 0.7 1.31 1.6 0.722± 0.005 0.30± 0.01 0.93 16.0 0.532± 0.003 0.41± 0.0299 17.27± 1.11 0.7 1.36 1.6 0.502± 0.002 0.20± 0.01 1.01 16.0 0.382± 0.002 0.26± 0.02100 7.31± 0.38 0.7 1.24 1.6 0.771± 0.005 0.26± 0.02 0.85 16.0 0.545± 0.004 0.37± 0.02101 7.20± 0.33 0.7 1.24 1.6 0.781± 0.003 0.22± 0.01 0.84 16.0 0.551± 0.002 0.31± 0.01102 9.42± 1.11 0.7 1.28 1.6 0.488± 0.006 0.11± 0.01 0.90 16.0 0.353± 0.004 0.15± 0.02103 8.47± 0.91 0.7 1.27 1.6 0.516± 0.003 0.09± 0.01 0.88 16.0 0.370± 0.003 0.13± 0.01104 8.25± 0.74 0.7 1.26 1.6 0.538± 0.004 0.13± 0.01 0.87 16.0 0.385± 0.003 0.19± 0.02105 3.52± 1.32 0.7 1.13 1.6 0.397± 0.000 0.03± 0.01 0.67 16.0 0.253± 0.000 0.05± 0.02106 9.66± 0.41 0.7 1.28 1.6 1.135± 0.017 0.75± 0.05 0.90 16.0 0.825± 0.013 1.04± 0.06107 10.38± 0.67 0.7 1.29 1.6 0.599± 0.005 0.20± 0.01 0.92 16.0 0.438± 0.003 0.27± 0.02108 2.86± 0.41 0.7 1.10 1.6 0.644± 0.006 0.07± 0.01 0.62 16.0 0.392± 0.003 0.11± 0.02109 4.53± 0.81 0.7 1.17 1.6 0.500± 0.003 0.05± 0.01 0.74 16.0 0.332± 0.002 0.07± 0.01110 8.96± 1.35 0.7 1.27 1.6 0.451± 0.003 0.07± 0.01 0.89 16.0 0.325± 0.002 0.10± 0.01112 5.47± 1.00 0.7 1.20 1.6 0.451± 0.001 0.06± 0.01 0.78 16.0 0.308± 0.000 0.09± 0.02113 4.93± 0.41 0.7 1.19 1.6 0.657± 0.003 0.12± 0.01 0.76 16.0 0.442± 0.002 0.19± 0.02114 6.29± 0.98 0.7 1.22 1.6 0.471± 0.001 0.06± 0.01 0.81 16.0 0.327± 0.001 0.09± 0.01115 7.14± 0.37 0.7 1.24 1.6 0.699± 0.001 0.15± 0.01 0.84 16.0 0.492± 0.001 0.22± 0.01116 8.57± 0.99 0.7 1.27 1.6 0.494± 0.003 0.10± 0.01 0.88 16.0 0.355± 0.003 0.13± 0.02117 8.11± 0.60 0.7 1.26 1.6 0.575± 0.001 0.15± 0.01 0.87 16.0 0.411± 0.001 0.21± 0.02

We use the virial equation in the form

1

2I = Ωg + 2Ωk + Ωp, (18)

where I is the second derivative of the moment of inertiaI, Ωg is the gravitational potential energy of the core, Ωk

is the internal thermal energy of the core, and Ωp is theexternal pressure energy of the core. We do not include theinternal magnetic energy in the following analysis. A corewith I > 0 is virially unbound and dispersing, a core withI < 0 is virially bound and collapsing, and a core with I = 0is in virial equilibrium with its surroundings.

We determined external pressure energies for our coresusing the equation

Ωp = −4πPextr3e . (19)

We assume that 13CO traces material adjacent to our cores,and again assume that the cores are confined by externalpressure at a density of either 103 cm−3 or 104 cm−3, in bothcases at the radius re defined in Section 6.1 (see equations 11and 14). These bounding densities are chosen as representinga range of densities from a typical gas density traced by13CO (∼ 103 cm−3) to the gas density at which 13CO ceases

to be an effective tracer (∼ 104 cm−3; Di Francesco et al.2007), and as being a physically plausible density at whichour cores might be bounded (see discussion in Section 6.1,above).

We determined gravitational potential energies for eachof our cores using the equation for the gravitational poten-tial energy of a spherically symmetrical Gaussian densitydistribution truncated at a radius re:

Ωg = −16π2Gρ20α5

[√π

4erf

(reα

)

−√

π

2e−

1

2( re

α)2 erf

(

re

α√2

)

+1

2

reαe−(

re

α)2]

. (20)

where ρ0 is the modelled central density of the core and α isthe modelled Gaussian width of the core – see Pattle (2016)for a derivation of this result.

We were able to put a lower limit on the internal energyof each of our cores by estimating the thermal kinetic energyof the core,

Ωk,t =3

2Mc2s =

3

2M

kbT

µmh

. (21)

Pattle et al. (2015) found that a significant fraction of the

c© 2016 RAS, MNRAS 000, 1–29

24 K. Pattle et al.

Figure 16. The virial plane for our starless cores. Left panel: bounding density ne = 103 cm−3; right panel: bounding density ne =104 cm−3. Virial stability is plotted on the x axis. The ratio of gravitational potential energy to external pressure energy is plotted onthe y axis. The vertical dashed line indicates the line of virial stability, with the right-hand side of the plot being bound and the leftside being unbound. The horizontal dashed line marks equipartition between external pressure energy and gravitational potential energy;cores above the line are gravitationally bound, while cores below the line are pressure-confined. Closed circles indicate cores with a massgreater than their BE-critical mass. Colour coding as in Figure 9 (red – L1147/58; light green – L1172; dark green – L1174; blue – L1251;purple – L1228).

internal kinetic energy of starless cores in the Ophiuchusmolecular cloud is non-thermal. Unless starless cores inCepheus are substantially dissimilar to those in Ophiuchus,there is likely to be a substantial non-thermal component tothe internal energy of our cores. Hence the values given byequation 21 are a lower limit on the true value of Ωk. Thevalues of Ωg, Ωp, Ωk and the virial parameter 1

2I which we

determine are listed in Table 8.

7.2 Virial stability of cores in Cepheus

Our best estimate of the virial plane for Cepheus is shownin Figure 16. The virial plane diagram was introduced byPattle et al. (2015) as a means of assessing the virial stabil-ity and mode of confinement of starless cores. The abcissashows the virial ratio, −(Ωg+Ωp)/2Ωk. Cores to the right ofthe vertical dashed line in the virial plane are virially bound,while cores to the left of this line are virially unbound. Theordinate shows the ratio of gravitational potential energyto external pressure energy, Ωg/Ωp. The dominant mode ofconfinement of cores below the horizontal dashed line is ex-ternal pressure, while the dominant mode of confinement ofcores above this line is self-gravity.

It must be stressed that the values shown for the virialratio −(Ωg + Ωp)/2Ωk are upper limits (for the assumedbounding density); Figure 16 shows the greatest extent towhich our cores could be virially bound.

Figure 16 suggests that in the high-bounding-densitycase, our cores are not thermally supported: in the absenceof non-thermal internal energy and/or an internal magneticfield, −(Ωg+Ωp) > 2Ωk in all but one case (core 19, which is

marginally unbound). If the cores’ dominant support mech-anism were internal thermal motions, then all but two ofour cores (core 19, and core 3, discussed below) would besimultaneously undergoing pressure-driven collapse.

The physical picture in the low-bounding-density case,is less clear than in the high-density case. In this case, thecores are less strongly bound and less pressure-confined thanin the high-density case. Figure 16 shows that our cores re-main typically virially bound and pressure-confined in thelow-bounding-density-case, but that a significant fractionof the cores are in or near virial equlibrium, particularlythose in L1147/58, L1174 and L1228. Many of the coresin L1147/58 are marginally unbound in this analysis, alongwith four cores in L1174 and one core in L1228. All of thecores in L1251 and L1172 remain virially bound. In this case,there are seven gravitationally- and virially-bound cores inthe sample, and one core which is gravitationally-dominatedbut marginally virially unbound.

In either case, these results suggest that a significantfraction of our cores are simultaneously undergoing pressure-driven collapse. As this scenario is unlikely, we hypothesisethree possible alternative scenarios:

(1) The Y97 measurements overestimate the externalpressure on our cores. If the low-resolution, and hence large-scale, Y97 13CO measurements do not correspond accu-rately to the gas immediately surrounding our dense cores,the linewidths measured by Y97 will not accurately repre-sent the pressure confining the core. As turbulent motionsare expected to dissipate on small scales (e.g. Larson 1981;Solomon et al. 1987), velocities measured with the Y97 beamsize of 2.4 arcmin (corresponding to 12 pc at a distance of

c© 2016 RAS, MNRAS 000, 1–29

First SCUBA-2 observations of Cepheus 25

Table 8. Terms in the virial equation for cores in Cepheus: (1)core ID, (2) thermal internal energy (3,4,5) gravitational potentialenergy, external pressure energy from 13CO measurements, andthe virial parameter, for a bounding density of n(H2)= 103 cm−3,(6,7,8) as 3–5 for a bounding density of n(H2) = 104 cm−3.

n(H2)= 103 cm−3 n(H2)= 104 cm−3

Source Ωk Ωg Ωp

12I Ωg Ωp

12I

ID (×1041 erg)

3 13.0 -28.04 -4.3 -6.4 -30.08 -20.2 -24.44 15.4 -29.27 -13.1 -11.5 -36.49 -47.1 -52.77 2.6 -1.14 -2.6 +1.5 -1.56 -8.2 -4.58 3.2 -1.42 -4.4 +0.6 -2.23 -10.7 -6.59 1.7 -0.53 -1.9 +1.0 -0.75 -5.4 -2.810 2.6 -1.14 -2.6 +1.4 -1.55 -8.2 -4.512 1.2 -0.24 -1.9 +0.2 -0.42 -3.7 -1.813 1.5 -0.43 -1.9 +0.7 -0.65 -5.1 -2.714 1.3 -0.33 -1.5 +0.7 -0.48 -4.2 -2.115 1.2 -0.24 -1.4 +0.7 -0.37 -3.6 -1.616 0.7 -0.08 -1.1 +0.2 -0.15 -1.8 -0.517 0.8 -0.17 -1.0 +0.6 -0.24 -2.8 -1.318 6.3 -4.00 -11.9 -3.3 -7.51 -18.9 -13.819 0.4 -0.03 -0.9 -0.1 -0.06 -0.6 +0.220 9.0 -7.78 -13.3 -3.0 -12.75 -30.0 -24.721 11.7 -13.24 -6.2 +4.0 -14.10 -30.0 -20.626 12.5 -27.02 -8.2 -10.2 -28.50 -40.4 -43.927 11.9 -5.42 -19.1 -0.8 -7.67 -56.0 -39.928 1.4 -0.13 -2.6 +0.1 -0.20 -6.4 -3.829 1.8 -0.12 -3.1 +0.4 -0.21 -6.4 -3.030 1.3 -0.18 -3.7 -1.3 -0.29 -7.9 -5.731 2.0 -0.42 -5.4 -1.8 -0.67 -13.2 -9.833 0.6 -0.02 -1.7 -0.4 -0.04 -1.5 -0.334 3.1 -0.55 -6.7 -1.1 -0.89 -15.6 -10.336 1.7 -0.27 -3.0 +0.2 -0.37 -9.0 -5.937 1.0 -0.11 -3.1 -1.2 -0.20 -6.1 -4.338 3.9 -0.77 -9.8 -2.7 -1.35 -19.0 -12.539 3.2 -0.34 -8.1 -2.1 -0.68 -9.3 -3.640 10.0 -3.28 -38.2 -21.5 -6.68 -21.1 -7.742 1.0 -0.16 -2.7 -0.9 -0.23 -7.1 -5.443 1.0 -0.06 -2.2 -0.3 -0.11 -4.3 -2.544 2.4 -0.34 -6.6 -2.2 -0.62 -11.2 -7.145 1.2 -0.07 -2.9 -0.5 -0.14 -4.2 -2.046 1.7 -0.28 -4.2 -1.0 -0.44 -10.3 -7.349 1.1 -0.23 -3.0 -1.1 -0.34 -8.7 -6.950 0.8 -0.12 -2.5 -1.0 -0.19 -6.3 -4.851 0.8 -0.12 -2.9 -1.4 -0.20 -6.4 -4.952 1.1 -0.20 -3.3 -1.4 -0.31 -8.4 -6.653 0.9 -0.13 -3.3 -1.7 -0.23 -6.6 -5.154 0.7 -0.11 -2.5 -1.1 -0.17 -5.9 -4.655 2.6 -0.97 -6.9 -2.7 -1.39 -20.1 -16.358 11.1 -23.88 -12.5 -14.1 -25.42 -60.3 -63.459 7.5 -8.19 -9.4 -2.7 -8.97 -42.7 -36.7

60 37.5 -162.68 -76.0 -163.7 -184.08 -322.0 -431.162 5.1 -5.42 -10.2 -5.4 -6.16 -43.0 -38.963 14.9 -25.21 -45.5 -40.8 -31.79 -160.5 -162.464 9.3 -19.56 -12.3 -13.3 -20.97 -58.3 -60.765 3.2 -1.75 -11.0 -6.3 -2.32 -36.1 -31.966 8.3 -10.89 -18.1 -12.4 -12.66 -73.0 -69.167 1.8 -0.67 -5.3 -2.5 -0.86 -18.6 -15.968 8.0 -9.26 -19.0 -12.3 -11.03 -73.6 -68.670 1.2 -0.28 -4.6 -2.4 -0.40 -13.3 -11.371 19.4 -50.83 -37.4 -49.4 -57.43 -158.8 -177.472 3.0 -1.66 -10.5 -6.0 -2.18 -34.5 -30.673 1.0 -0.16 -4.7 -3.0 -0.26 -10.5 -8.974 2.0 -0.65 -7.8 -4.5 -0.93 -22.4 -19.475 2.2 -0.99 -7.8 -4.3 -1.31 -25.6 -22.477 1.1 -0.18 -5.6 -3.6 -0.32 -11.4 -9.6

Table 8. – continued.

n(H2)= 103 cm−3 n(H2)= 104 cm−3

Source Ωk Ωg Ωp

12I Ωg Ωp

12I

ID (×1041 erg)

78 2.9 -1.18 -12.0 -7.4 -1.74 -33.0 -28.979 1.0 -0.14 -5.1 -3.4 -0.25 -9.8 -8.180 2.0 -0.62 -7.1 -3.6 -0.87 -21.2 -18.081 0.9 -0.13 -3.9 -2.3 -0.21 -9.3 -7.783 1.0 -0.23 -3.5 -1.8 -0.31 -11.1 -9.485 0.8 -0.12 -5.1 -3.6 -0.23 -8.7 -7.386 1.7 -0.54 -6.4 -3.5 -0.75 -19.4 -16.687 0.9 -0.16 -4.2 -2.5 -0.25 -10.3 -8.788 1.6 -0.33 -10.2 -7.5 -0.63 -14.3 -11.989 1.8 -0.48 -9.3 -6.3 -0.79 -20.3 -17.690 3.0 -1.28 -12.5 -7.9 -1.88 -34.5 -30.592 1.4 -0.34 -4.7 -2.4 -0.47 -14.5 -12.293 17.7 -34.67 -55.4 -54.6 -43.79 -195.0 -203.494 1.3 -0.30 -6.2 -3.9 -0.47 -15.1 -12.995 19.2 -32.43 -73.5 -67.5 -44.88 -223.8 -230.3

96 5.8 -3.49 -24.0 -15.9 -5.22 -64.1 -57.897 1.8 -0.48 -9.5 -6.3 -0.81 -20.4 -17.598 2.2 -0.98 -4.1 -0.7 -1.20 -15.1 -11.999 1.0 -0.30 -1.4 +0.3 -0.34 -5.7 -4.0100 2.0 -0.76 -5.1 -1.8 -1.02 -16.1 -13.0101 1.8 -0.57 -4.3 -1.2 -0.77 -13.6 -10.7102 0.6 -0.09 -1.1 -0.1 -0.11 -3.9 -2.9103 0.5 -0.07 -1.1 -0.1 -0.09 -3.6 -2.6104 0.7 -0.14 -1.7 -0.3 -0.18 -5.5 -4.2105 0.1 -0.01 -0.5 -0.2 -0.01 -1.0 -0.7106 8.3 -9.13 -18.0 -10.4 -11.58 -62.8 -57.7107 1.2 -0.34 -2.3 -0.3 -0.43 -8.4 -6.4108 0.5 -0.05 -2.0 -1.0 -0.08 -3.4 -2.5109 0.3 -0.02 -0.8 -0.3 -0.03 -2.1 -1.6110 0.4 -0.04 -0.7 -0.0 -0.05 -2.3 -1.7112 0.3 -0.02 -0.8 -0.3 -0.04 -2.3 -1.7113 0.9 -0.15 -2.6 -1.1 -0.23 -6.9 -5.4114 0.3 -0.03 -0.8 -0.2 -0.04 -2.4 -1.8115 1.2 -0.26 -2.7 -0.6 -0.35 -8.5 -6.5116 0.5 -0.07 -1.1 -0.1 -0.09 -3.6 -2.7117 0.9 -0.19 -2.0 -0.5 -0.24 -6.6 -5.1

300 pc) may not be representative of the velocities of mate-rial surrounding the sub-parsec-scale cores we consider here.

(2) The non-thermal motions of the gas surroundingthe core do not create the effect of a hydrostatic pressureon the core, or do not do so in such a manner that themeasured linewidth accurately represents the pressure onthe core caused by non-thermal gas motions (see, e.g., MacLow & Klessen 2004).

(3) The dominant mechanism of core support inCepheus has not been accounted for in our virial analy-sis. In this scenario, cores are predominantly supported bysome combination of internal non-thermal motions and/orinternal magnetic field. Pattle et al. (2015) found that themajority of the starless cores in the highest-column-densityregions of the Ophiuchus molecular cloud were typically inapproximate virial equilibrium with their surroundings, andmarginally pressure-dominated, with the majority of sup-port against collapse provided by non-thermal internal mo-tions. Figure 16 is consistent with starless cores in Cepheusbehaving in a similar way to those in Ophiuchus, presumingthat there is sufficient internal support from non-thermalinternal motions and/or internal magnetic fields to bring

c© 2016 RAS, MNRAS 000, 1–29

26 K. Pattle et al.

the cores into approximate virial equilibrium with their sur-roundings.

None of these hypotheses are contradictory, and all maycontribute to the apparent over-estimation of the degree towhich our cores are pressure-confined.

Values of the virial ratio are marked as upper limits onFigure 16, as we can identify the information missing fromour determination of the cores’ virial ratios: an estimate ofthe cores’ non-thermal and magnetic internal energies. If ei-ther hypotheses (1) or (2) above are valid, then the values ofthe confinement ratio Ωg/Ωp shown on Figure 16 are lowerlimits on the true values. However, we do not mark them assuch on Figure 16, as we do not know which of our hypothe-ses best explain the measured values of external pressure.

The high-density analysis suggests that there is onegravitationally-bound prestellar core amongst our sample:core 3 in L1147/58, for which Ωg > Ωp and −(Ωg + Ωp) >2Ωk. This core is among the 13 cores predicted to be gravita-tionally unstable by the Bonnor-Ebert criterion. It is worthnoting that the majority of the cores which are only mildlypressure-dominated are unstable according to the Bonnor-Ebert criterion. If the measured values of the confinementratio are in fact lower limits on the true values, many ofthese cores may be prove to be gravitationally bound.

The low-density analysis suggests that there are sevengravitationally-bound prestellar cores amongst our sample,all of which are unstable according to the Bonnor-Ebertcriterion. Three of the cores which are mildly pressure-dominated are unstable according to the Bonnor-Ebert cri-terion.

The Bonnor-Ebert stability criterion is in better agree-ment with our virial analysis in the low-density case thanin the high-density case. If the Bonnor-Ebert criterion is infact an accurate measure of the stability of our cores, it sug-gests that the low-density model (ne = 103 cm−3) is a moreaccurate description of the energy balance of our cores thanthe high-density model.

That the low-density model is more likely to be accurateis also supported by the values of the virial ratio shown inFigure 16: in the low-density case, a significant fraction ofthe cores have virial ratios consistent with their being in ornear virial equilibrium with their surroundings, as might beexpected in reasonably long-lived star-forming regions (all ofthe Cepheus clouds have been forming stars for long enoughto form at least some Class II protostars; see K09).

In the high-density case, almost all of the cores appearto be strongly pressure-confined and virially bound, suggest-ing that they are all effectively imploding under pressure -an unlikely situation for cores in star-forming regions thatappear to have been forming stars continuously for a signif-icant length of time, particularly those showing no signs ofrecent external influence. Hence, we conclude that of our twomodels, a density of 103 cm−3 is the more likely to be repre-sentative of the true density at which our cores are confinedby pressure from the surrounding molecular cloud.

7.3 Resolving the virial balance of cores in

Cepheus

The minimum additional information which is required inorder to determine which of our cores are in fact viriallybound is a measure of the cores’ internal linewidths, i.e.

observations of the cores in an optically thin dense gas tracersuch as C18O or nitrogen-bearing tracers (e.g. NH3, N2H

+).This would allow determination of the level of core supportfrom non-thermal internal motions.

Ideally, a measure of the magnetic field strength in thecores is also required, to determine whether magnetic fieldsplay a significant role in core support in Cepheus. This mightbe achieved using a wide-field polarimeter such as POL-2 onthe JCMT (Friberg et al. 2016; Ward-Thompson et al. 2016,in prep.).

Our estimates of the external surface pressure on thecores could be improved with higher-resolution observationsof the Cepheus Flare clouds in medium-density tracers suchas 13CO. Measurements of the linewidth of gas surround-ing the cores taken with an instrument with angular resolu-tion comparable to the angular size of the cores (e.g. usingHARP-B on the JCMT; Buckle et al. 2010) would allow usto exclude hypothesis (1), above.

8 SUMMARY

In this paper we have extracted sources from the SCUBA-2data of the L1147/L1158, L1172/L1174, L1251 and L1228regions of the Cepheus Flare. We have characterised oursources using their 850-µm flux densities and temperaturessupplied by the Herschel GBS (Di Francesco et al., 2016,in prep.). We have compared the properties of cores in thedifferent Cepheus Flare regions in order to determine themode of star formation proceeding in each region. We havedetermined the relative importance of gravity and externalpressure in confining our cores, and have determined an up-per limit on the degree to which our cores are virially bound.

We identified 117 sources across the Cepheus Flare re-gion using the CSAR source extraction algorithm, of which23 were associated with a protostar in the K09 Spitzer cata-logue. Of our 117 sources, 20 were located in L1147/L1158,26 in L1174, 9 sources in L1172, 42 in L1251 and 20 in L1228.We determined the best-fit flux densities of our sources usingthe multiple-Gaussian fitting algorithm described by Pattleet al. (2015).

We determined masses for each of our sources usingour best-fit flux densities and temperatures supplied by theHerschel GBS (Di Francesco et al., 2016, in prep.). We foundthat our cores typically lie in the ‘prestellar’ part of themass/size plane. Our cores typically have temperatures inthe range ∼ 9− 15K, with the exception of cores associatedwith the L1174 reflection nebula, which have temperaturesup to ∼ 30K.

We determined source temperatures from the ratio ofSCUBA-2 450-µm and 850-µm flux densities, for those ofour sources with a detection > 5σ at 450µm. We foundthat temperatures determined from Herschel and SCUBA-2 data were generally in agreement for our sources. Wefound a slight tendency for Herschel -derived temperaturesto be higher than SCUBA-2-derived temperatures, consis-tent with Herschel observations sampling slightly warmermaterial. Source masses derived from SCUBA-2 temper-atures are correspondingly slightly higher than those de-rived from Herschel temperatures. We concluded that theSCUBA-2 flux density ratio is a reliable determinant of asource’s temperature when neither the 450-µm nor the 850-

c© 2016 RAS, MNRAS 000, 1–29

First SCUBA-2 observations of Cepheus 27

µm data point is on the Rayleigh-Jeans tail of a source’sspectral energy distribution – i.e. when T . 20K.

We analysed the cumulative distribution functions ofcore masses for each region in Cepheus, using the maxi-mum likelihood estimator for an infinite power-law distribu-tion, and found that the core mass function in each regionshows a sub-Salpeter power-law behaviour, with the excep-tion of L1228, which has a power-law index consistent withthe Salpeter IMF. Determining the power-law index over allcores, we found a sub-Salpeter value of α = 1.88± 0.09 overthe mass range M > 0.08M⊙. For the highest-mass cores,we found a CMF power-law index α = 2.61 ± 0.27 over themass range M > 0.5M⊙ (again determined over all cores),marginally consistent with the Salpeter IMF.

We compared the number of starless cores detected ineach region with the numbers of embedded and Class IIsources found by K09. We found that L1147/L1158 andL1228 have a high ratio of starless cores to Class II sources,while L1251 and L1174 have a low ratio. This is consistentwith L1174 and L1251 being active sites of star formation,while L1147/L1158 and L1228 form stars in a less activemode.

We determined the Bonnor-Ebert critically-stablemasses of our cores, and found that the Bonnor-Ebert modelpredicts that most of our cores have stable BE solutions ac-cessible to them.

We performed a virial analysis on our cores, determin-ing the external pressure on our cores using 13CO veloc-ity dispersion measurements determined by Yonekura et al.(1997). We found that, assuming a bounding density for ourcores of 104 cm−3, all but one of our cores are virially boundand there is only one gravitationally-bound prestellar coreamong our sample, with the rest of the cores being confinedby external pressure. However, we found that if we assume abounding density of 103 cm−3, seven of our cores are gravi-tationally bound, and the majority of the cores are approxi-mately virialised or mildly pressure-confined. We concludedthat, if the Yonekura et al. (1997) measurements are rep-resentative of the conditions in the gas confining our cores,our cores typically cannot be supported by internal ther-

mal energy alone. In the absence of non-thermal internalmotions or an internal magnetic field, a significant fractionof our cores would be significantly out of virial equilibriumand collapsing under pressure. We hence hypothesise thatcores in the Cepheus molecular cloud may not typically bethermally supported.

9 ACKNOWLEDGEMENTS

K.P. wishes to acknowledge STFC postdoctoral support un-der grant numbers ST/K002023/1 and ST/M000877/1 andstudentship support under grant number ST/K501943/1while this research was carried out. The James ClerkMaxwell Telescope has historically been operated by theJoint Astronomy Centre on behalf of the Science and Tech-nology Facilities Council of the United Kingdom, the Na-tional Research Council of Canada and the NetherlandsOrganisation for Scientific Research. Additional funds forthe construction of SCUBA-2 were provided by the CanadaFoundation for Innovation. The Starlink software (Currieet al. 2014) is supported by the East Asian Observatory.

This research used the services of the Canadian AdvancedNetwork for Astronomy Research (CANFAR) which in turnis supported by CANARIE, Compute Canada, University ofVictoria, the National Research Council of Canada, and theCanadian Space Agency. This research used the facilities ofthe Canadian Astronomy Data Centre operated by the Na-tional Research Council of Canada with the support of theCanadian Space Agency. Herschel is an ESA space obser-vatory with science instruments provided by European-ledPrincipal Investigator consortia and with important partici-pation from NASA. This research has made use of the NASAAstrophysics Data System. The authors wish to recognizeand acknowledge the very significant cultural role and rev-erence that the summit of Maunakea has always had withinthe indigenous Hawaiian community. We are most fortunateto have the opportunity to conduct observations from thismountain.

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1Jeremiah Horrocks Institute, University of Central Lan-cashire, Preston, Lancashire, PR1 2HE, UK2Department of Physics and Astronomy, University of Vic-toria, Victoria, BC, V8P 1A1, Canada3NRC Herzberg Astronomy and Astrophysics, 5071 WestSaanich Rd, Victoria, BC, V9E 2E7, Canada4Leiden Observatory, Leiden University, PO Box 9513, 2300RA Leiden, The Netherlands5Max Planck Institute for Astronomy, Konigstuhl 17, D-69117 Heidelberg, Germany6Astrophysics Group, Cavendish Laboratory, J J ThomsonAvenue, Cambridge, CB3 0HE7Kavli Institute for Cosmology, Institute of Astronomy, Uni-versity of Cambridge, Madingley Road, Cambridge, CB30HA, UK8Department of Physics and Astronomy, University of Wa-terloo, Waterloo, Ontario, N2L 3G1, Canada9Joint Astronomy Centre, 660 N. A‘ohoku Place, UniversityPark, Hilo, Hawaii 96720, USA

c© 2016 RAS, MNRAS 000, 1–29

First SCUBA-2 observations of Cepheus 29

10Physics and Astronomy, University of Exeter, StockerRoad, Exeter EX4 4QL, UK11LSST Project Office, 933 N. Cherry Ave, Tucson, AZ85719, USA12School of Physics and Astronomy, Cardiff University, TheParade, Cardiff, CF24 3AA, UK13European Southern Observatory (ESO), Garching, Ger-many14Jodrell Bank Centre for Astrophysics, Alan Turing Build-ing, School of Physics and Astronomy, University of Manch-ester, Oxford Road, Manchester, M13 9PL, UK15Institute for Astronomy, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland16Universite de Montreal, Centre de Recherche en Astro-physique du Quebec et departement de physique, C.P. 6128,succ. centre-ville, Montreal, QC, H3C 3J7, Canada17James Madison University, Harrisonburg, Virginia 22807,USA18School of Physics, Astronomy & Mathematics, Universityof Hertfordshire, College Lane, Hatfield, HERTS AL10 9AB,UK19Astrophysics Research Institute, Liverpool John MooresUniversity, Egerton Warf, Birkenhead, CH41 1LD, UK20Imperial College London, Blackett Laboratory, PrinceConsort Rd, London SW7 2BB, UK21Dept of Physics & Astronomy, University of Manitoba,Winnipeg, Manitoba, R3T 2N2 Canada22Dunlap Institute for Astronomy & Astrophysics, Univer-sity of Toronto, 50 St. George St., Toronto ON M5S 3H4Canada23Dept. of Physical Sciences, The Open University, MiltonKeynes MK7 6AA, UK24The Rutherford Appleton Laboratory, Chilton, Didcot,OX11 0NL, UK.25UK Astronomy Technology Centre, Royal Observatory,Blackford Hill, Edinburgh EH9 3HJ, UK26Institute for Astronomy, Royal Observatory, University ofEdinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK27Centre de recherche en astrophysique du Quebec etDepartement de physique, de genie physique et d’optique,Universite Laval, 1045 avenue de la medecine, Quebec, G1V0A6, Canada28Department of Physics and Astronomy, UCL, Gower St,London, WC1E 6BT, UK29Department of Physics and Astronomy, McMaster Univer-sity, Hamilton, ON, L8S 4M1, Canada30Department of Physics, University of Alberta, Edmonton,AB T6G 2E1, Canada31University of Western Sydney, Locked Bag 1797, PenrithNSW 2751, Australia32National Astronomical Observatory of China, 20A DatunRoad, Chaoyang District, Beijing 100012, China

c© 2016 RAS, MNRAS 000, 1–29